diff --git a/Tests/test_file_bmp.py b/Tests/test_file_bmp.py
index bfe24e0007d..f214fd6bda1 100644
--- a/Tests/test_file_bmp.py
+++ b/Tests/test_file_bmp.py
@@ -147,6 +147,25 @@ def test_rle8():
                 im.load()
 
 
+@pytest.mark.parametrize(
+    "file_name,length",
+    (
+        # EOF immediately after the header
+        ("Tests/images/hopper_rle8.bmp", 1078),
+        # EOF during delta
+        ("Tests/images/bmp/q/pal8rletrns.bmp", 3670),
+        # EOF when reading data in absolute mode
+        ("Tests/images/bmp/g/pal8rle.bmp", 1064),
+    ),
+)
+def test_rle8_eof(file_name, length):
+    with open(file_name, "rb") as fp:
+        data = fp.read(length)
+        with Image.open(io.BytesIO(data)) as im:
+            with pytest.raises(ValueError):
+                im.load()
+
+
 def test_offset():
     # This image has been hexedited
     # to exclude the palette size from the pixel data offset
diff --git a/src/PIL/BmpImagePlugin.py b/src/PIL/BmpImagePlugin.py
index 7221d7f065e..7e7e742cd74 100644
--- a/src/PIL/BmpImagePlugin.py
+++ b/src/PIL/BmpImagePlugin.py
@@ -283,8 +283,11 @@ def decode(self, buffer):
         data = bytearray()
         x = 0
         while len(data) < self.state.xsize * self.state.ysize:
-            num_pixels = self.fd.read(1)[0]
+            pixels = self.fd.read(1)
             byte = self.fd.read(1)
+            if not pixels or not byte:
+                break
+            num_pixels = pixels[0]
             if num_pixels:
                 # encoded mode
                 if x + num_pixels > self.state.xsize:
@@ -303,12 +306,18 @@ def decode(self, buffer):
                     break
                 elif byte[0] == 2:
                     # delta
+                    bytes_read = self.fd.read(2)
+                    if len(bytes_read) < 2:
+                        break
                     right, up = self.fd.read(2)
                     data += b"\x00" * (right + up * self.state.xsize)
                     x = len(data) % self.state.xsize
                 else:
                     # absolute mode
-                    data += self.fd.read(byte[0])
+                    bytes_read = self.fd.read(byte[0])
+                    data += bytes_read
+                    if len(bytes_read) < byte[0]:
+                        break
                     x += byte[0]
 
                     # align to 16-bit word boundary