diff --git a/Tests/test_file_psd.py b/Tests/test_file_psd.py
index 8f2ca58a662..da572ae6338 100644
--- a/Tests/test_file_psd.py
+++ b/Tests/test_file_psd.py
@@ -85,6 +85,11 @@ def test_eoferror() -> None:
         # Test that seeking to the last frame does not raise an error
         im.seek(n_frames - 1)
 
+    # Test seeking past the last frame without calling n_frames first
+    with Image.open(test_file) as im:
+        with pytest.raises(EOFError):
+            im.seek(3)
+
 
 def test_seek_tell() -> None:
     with Image.open(test_file) as im:
diff --git a/src/PIL/PsdImagePlugin.py b/src/PIL/PsdImagePlugin.py
index 69a8703dd8b..dd3d5ab95fd 100644
--- a/src/PIL/PsdImagePlugin.py
+++ b/src/PIL/PsdImagePlugin.py
@@ -175,6 +175,9 @@ def seek(self, layer: int) -> None:
             raise self._fp.ex
 
         # seek to given layer (1..max)
+        if layer > len(self.layers):
+            msg = "no more images in PSD file"
+            raise EOFError(msg)
         _, mode, _, tile = self.layers[layer - 1]
         self._mode = mode
         self.tile = tile