diff --git a/skimage/feature/peak.py b/skimage/feature/peak.py
index 30e1a84b..ebacfa3a 100644
--- a/skimage/feature/peak.py
+++ b/skimage/feature/peak.py
@@ -32,6 +32,8 @@ def peak_local_max(image, min_distance=10, threshold='deprecated',
     coordinates : (N, 2) array
         (row, column) coordinates of peaks.
     """
+    if np.all(image == image.flat[0]):
+        return []
     image = image.copy()
     # Non maximum filter
     size = 2 * min_distance + 1
diff --git a/skimage/feature/tests/test_peak.py b/skimage/feature/tests/test_peak.py
index 7f960e3b..7fb090ba 100644
--- a/skimage/feature/tests/test_peak.py
+++ b/skimage/feature/tests/test_peak.py
@@ -36,6 +36,13 @@ def test_absolute_threshold():
     assert len(peaks) == 1
     assert_close(peaks, [(3, 3)])
 
+
+def test_constant_image():
+    image = 128 * np.ones((20, 20), dtype=np.uint8)
+    peaks = peak.peak_local_max(image, min_distance=1)
+    assert len(peaks) == 0
+
+
 if __name__ == '__main__':
     from numpy import testing
     testing.run_module_suite()