diff --git a/src/PIL/TarIO.py b/src/PIL/TarIO.py
index 779288b1c..86490a496 100644
--- a/src/PIL/TarIO.py
+++ b/src/PIL/TarIO.py
@@ -35,12 +35,16 @@ class TarIO(ContainerIO.ContainerIO[bytes]):
         while True:
             s = self.fh.read(512)
             if len(s) != 512:
+                self.fh.close()
+
                 msg = "unexpected end of tar file"
                 raise OSError(msg)
 
             name = s[:100].decode("utf-8")
             i = name.find("\0")
             if i == 0:
+                self.fh.close()
+
                 msg = "cannot find subfile"
                 raise OSError(msg)
             if i > 0: