diff --git a/nibabel/loadsave.py b/nibabel/loadsave.py
index 1dc576498b..c239c1a568 100644
--- a/nibabel/loadsave.py
+++ b/nibabel/loadsave.py
@@ -9,7 +9,7 @@
 # module imports
 """ Utilities to load and save image objects """
 
-import os.path as op
+import os
 import numpy as np
 
 from .filename_parser import splitext_addext
@@ -36,8 +36,12 @@ def load(filename, **kwargs):
     img : ``SpatialImage``
        Image of guessed type
     '''
-    if not op.exists(filename):
-        raise FileNotFoundError("No such file: '%s'" % filename)
+    try:
+        stat_result = os.stat(filename)
+    except OSError:
+        raise FileNotFoundError("No such file or no access: '%s'" % filename)
+    if stat_result.st_size <= 0:
+        raise ImageFileError("Empty file: '%s'" % filename)
     sniff = None
     for image_klass in all_image_classes:
         is_valid, sniff = image_klass.path_maybe_image(filename, sniff)
diff --git a/nibabel/tests/test_loadsave.py b/nibabel/tests/test_loadsave.py
index a5f36100d9..676c09c121 100644
--- a/nibabel/tests/test_loadsave.py
+++ b/nibabel/tests/test_loadsave.py
@@ -58,6 +58,14 @@ def test_file_not_found():
     assert_raises(FileNotFoundError, load, 'does_not_exist.nii.gz')
 
 
+def test_load_empty_image():
+    with InTemporaryDirectory():
+        open('empty.nii', 'w').close()
+        with assert_raises(ImageFileError) as err:
+            load('empty.nii')
+    assert_true(err.exception.args[0].startswith('Empty file: '))
+
+
 def test_read_img_data_nifti():
     shape = (2, 3, 4)
     data = np.random.normal(size=shape)