diff --git a/net-lib/net/qp.rkt b/net-lib/net/qp.rkt
index 779f6831c4..0c138e9d4c 100644
--- a/net-lib/net/qp.rkt
+++ b/net-lib/net/qp.rkt
@@ -77,6 +77,9 @@
                   (loop (read-byte in))
                   ;; Not a LF? Well, ok.
                   (loop next-next)))]
+             [(eof-object? next)
+              (warning "Illegal qp sequence: `='")
+              (display "=" out)]
              [(hex-digit? next)
               (let ([next-next (read-byte in)])
                 (cond [(eof-object? next-next)
diff --git a/net-test/tests/net/encoders.rkt b/net-test/tests/net/encoders.rkt
index 292ae94baa..c9c3931dcf 100644
--- a/net-test/tests/net/encoders.rkt
+++ b/net-test/tests/net/encoders.rkt
@@ -79,7 +79,8 @@
    do (check-same-all base64-encode-stream
                       base64-decode-stream
                       #rx#"^[0-9a-zA-Z+=/]*$"
-                      72)))
+                      72))
+  (test (qp-decode #"=20=") #" ="))
 
 #|
 Use this to compare base64 encode/decode against the unix utilities