diff --git a/Tests/images/input_bw_five_bands.fpx b/Tests/images/input_bw_five_bands.fpx
new file mode 100644
index 000000000..5fcb144ae
Binary files /dev/null and b/Tests/images/input_bw_five_bands.fpx differ
diff --git a/Tests/test_file_fpx.py b/Tests/test_file_fpx.py
index 7c985be30..25a7ff24b 100644
--- a/Tests/test_file_fpx.py
+++ b/Tests/test_file_fpx.py
@@ -1,5 +1,7 @@
 import unittest
 
+from PIL import Image
+
 from .helper import PillowTestCase
 
 try:
@@ -20,3 +22,7 @@ class TestFileFpx(PillowTestCase):
         # Test a valid OLE file, but not an FPX file
         ole_file = "Tests/images/test-ole-file.doc"
         self.assertRaises(SyntaxError, FpxImagePlugin.FpxImageFile, ole_file)
+
+    def test_fpx_invalid_number_of_bands(self):
+        with self.assertRaisesRegex(IOError, "Invalid number of bands"):
+            Image.open("Tests/images/input_bw_five_bands.fpx")
diff --git a/src/PIL/FpxImagePlugin.py b/src/PIL/FpxImagePlugin.py
index 3938f0f09..8d252c79c 100644
--- a/src/PIL/FpxImagePlugin.py
+++ b/src/PIL/FpxImagePlugin.py
@@ -97,7 +97,10 @@ class FpxImageFile(ImageFile.ImageFile):
         s = prop[0x2000002 | id]
 
         colors = []
-        for i in range(i32(s, 4)):
+        bands = i32(s, 4)
+        if bands > 4:
+            raise IOError("Invalid number of bands")
+        for i in range(bands):
             # note: for now, we ignore the "uncalibrated" flag
             colors.append(i32(s, 8 + i * 4) & 0x7FFFFFFF)