diff --git a/src/decoder/image.rs b/src/decoder/image.rs
index c22f963..c678da8 100644
--- a/src/decoder/image.rs
+++ b/src/decoder/image.rs
@@ -4,8 +4,8 @@ use super::stream::{
     PackBitsReader,
 };
 use super::tag_reader::TagReader;
+use super::{fp_predict_f32, fp_predict_f64, DecodingBuffer, Limits};
 use super::{stream::SmartReader, ChunkType};
-use super::{DecodingBuffer, Limits};
 use crate::tags::{CompressionMethod, PhotometricInterpretation, Predictor, SampleFormat, Tag};
 use crate::{ColorType, TiffError, TiffFormatError, TiffResult, TiffUnsupportedError};
 use std::convert::{TryFrom, TryInto};
@@ -406,6 +406,11 @@ impl Image {
                         TiffUnsupportedError::HorizontalPredictor(color_type),
                     ))
                 }
+                Predictor::FloatingPoint => {
+                    return Err(TiffError::UnsupportedError(
+                        TiffUnsupportedError::FloatingPointPredictor(color_type),
+                    ));
+                }
                 Predictor::__NonExhaustive => unreachable!(),
             },
             (type_, _) => {
@@ -423,6 +428,13 @@ impl Image {
                     TiffUnsupportedError::HorizontalPredictor(color_type),
                 ));
             }
+            (Predictor::FloatingPoint, DecodingBuffer::F32(_))
+            | (Predictor::FloatingPoint, DecodingBuffer::F64(_)) => {}
+            (Predictor::FloatingPoint, _) => {
+                return Err(TiffError::UnsupportedError(
+                    TiffUnsupportedError::FloatingPointPredictor(color_type),
+                ));
+            }
             _ => {}
         }
 
@@ -471,6 +483,24 @@ impl Image {
             if photometric_interpretation == PhotometricInterpretation::WhiteIsZero {
                 super::invert_colors(&mut buffer.subrange(0..total_samples), color_type);
             }
+        } else if padding.0 > 0 && self.predictor == Predictor::FloatingPoint {
+            // The floating point predictor shuffles the padding bytes into the encoded output, so
+            // this case is handled specially when needed.
+            for row in 0..(chunk_dimensions.1 - padding.1) {
+                let row_start = row * output_width * samples;
+                let row_end = row_start + (chunk_dimensions.0 - padding.0) * samples;
+
+                let mut encoded = vec![0u8; chunk_dimensions.0 * samples * byte_len];
+                reader.read_exact(&mut encoded)?;
+                match buffer.subrange(row_start..row_end) {
+                    DecodingBuffer::F32(buf) => fp_predict_f32(&mut encoded, buf, samples),
+                    DecodingBuffer::F64(buf) => fp_predict_f64(&mut encoded, buf, samples),
+                    _ => unreachable!(),
+                }
+                if photometric_interpretation == PhotometricInterpretation::WhiteIsZero {
+                    super::invert_colors(&mut buffer.subrange(row_start..row_end), color_type);
+                }
+            }
         } else {
             for row in 0..(chunk_dimensions.1 - padding.1) {
                 let row_start = row * output_width * samples;
diff --git a/src/decoder/mod.rs b/src/decoder/mod.rs
index 844cdaf..22face5 100644
--- a/src/decoder/mod.rs
+++ b/src/decoder/mod.rs
@@ -365,6 +365,36 @@ fn rev_hpredict_nsamp<T: Copy + Wrapping>(image: &mut [T], samples: usize) {
     }
 }
 
+pub fn fp_predict_f32(input: &mut [u8], output: &mut [f32], samples: usize) {
+    rev_hpredict_nsamp(input, samples);
+    for i in 0..output.len() {
+        // TODO: use f32::from_be_bytes() when we can (version 1.40)
+        output[i] = f32::from_bits(u32::from_be_bytes([
+            input[input.len() / 4 * 0 + i],
+            input[input.len() / 4 * 1 + i],
+            input[input.len() / 4 * 2 + i],
+            input[input.len() / 4 * 3 + i],
+        ]));
+    }
+}
+
+pub fn fp_predict_f64(input: &mut [u8], output: &mut [f64], samples: usize) {
+    rev_hpredict_nsamp(input, samples);
+    for i in 0..output.len() {
+        // TODO: use f64::from_be_bytes() when we can (version 1.40)
+        output[i] = f64::from_bits(u64::from_be_bytes([
+            input[input.len() / 8 * 0 + i],
+            input[input.len() / 8 * 1 + i],
+            input[input.len() / 8 * 2 + i],
+            input[input.len() / 8 * 3 + i],
+            input[input.len() / 8 * 4 + i],
+            input[input.len() / 8 * 5 + i],
+            input[input.len() / 8 * 6 + i],
+            input[input.len() / 8 * 7 + i],
+        ]));
+    }
+}
+
 fn fix_endianness_and_predict(
     mut image: DecodingBuffer,
     samples: usize,
@@ -389,6 +419,14 @@ fn fix_endianness_and_predict(
                 DecodingBuffer::F32(_) | DecodingBuffer::F64(_) => unreachable!(),
             }
         }
+        Predictor::FloatingPoint => {
+            let mut buffer_copy = image.as_bytes_mut().to_vec();
+            match image {
+                DecodingBuffer::F32(buf) => fp_predict_f32(&mut buffer_copy, buf, samples),
+                DecodingBuffer::F64(buf) => fp_predict_f64(&mut buffer_copy, buf, samples),
+                _ => unreachable!(),
+            }
+        }
         Predictor::__NonExhaustive => unreachable!(),
     }
 }
diff --git a/src/error.rs b/src/error.rs
index 45ea5b0..0f91ad8 100644
--- a/src/error.rs
+++ b/src/error.rs
@@ -134,6 +134,7 @@ impl fmt::Display for TiffFormatError {
 /// stability guarantees.
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub enum TiffUnsupportedError {
+    FloatingPointPredictor(ColorType),
     HorizontalPredictor(ColorType),
     InterpretationWithBits(PhotometricInterpretation, Vec<u8>),
     UnknownInterpretation,
@@ -154,6 +155,11 @@ impl fmt::Display for TiffUnsupportedError {
     fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(), fmt::Error> {
         use self::TiffUnsupportedError::*;
         match *self {
+            FloatingPointPredictor(color_type) => write!(
+                fmt,
+                "Floating point predictor for {:?} is unsupported.",
+                color_type
+            ),
             HorizontalPredictor(color_type) => write!(
                 fmt,
                 "Horizontal predictor for {:?} is unsupported.",
diff --git a/src/tags.rs b/src/tags.rs
index f0a2c07..04cb5ec 100644
--- a/src/tags.rs
+++ b/src/tags.rs
@@ -214,6 +214,7 @@ tags! {
 pub enum Predictor(u16) {
     None = 1,
     Horizontal = 2,
+    FloatingPoint = 3,
 }
 }
 
diff --git a/tests/decode_images.rs b/tests/decode_images.rs
index 5d947dc..df43524 100644
--- a/tests/decode_images.rs
+++ b/tests/decode_images.rs
@@ -494,3 +494,13 @@ fn timeout() {
 fn test_no_rows_per_strip() {
     test_image_sum_u8("no_rows_per_strip.tiff", ColorType::RGB(8), 99448840);
 }
+
+#[test]
+fn test_predictor_3_rgb_f32() {
+    test_image_sum_f32("predictor-3-rgb-f32.tif", ColorType::RGB(32), 54004.33);
+}
+
+#[test]
+fn test_predictor_3_gray_f32() {
+    test_image_sum_f32("predictor-3-gray-f32.tif", ColorType::Gray(32), 20008.275);
+}
diff --git a/tests/images/predictor-3-gray-f32.tif b/tests/images/predictor-3-gray-f32.tif
new file mode 100644
index 0000000..9fbda84
Binary files /dev/null and b/tests/images/predictor-3-gray-f32.tif differ
diff --git a/tests/images/predictor-3-rgb-f32.tif b/tests/images/predictor-3-rgb-f32.tif
new file mode 100644
index 0000000..d338f59
Binary files /dev/null and b/tests/images/predictor-3-rgb-f32.tif differ