diff --git a/Library/Homebrew/utils/curl.rb b/Library/Homebrew/utils/curl.rb
index 9f0d8f75d6..c330762435 100644
--- a/Library/Homebrew/utils/curl.rb
+++ b/Library/Homebrew/utils/curl.rb
@@ -38,7 +38,16 @@ def curl(*args)
 end
 
 def curl_download(*args, to: nil, **options)
-  curl("--location", "--remote-time", "--continue-at", "-", "--output", to, *args, **options)
+  continue_at ||= "-"
+  curl("--location", "--remote-time", "--continue-at", continue_at, "--output", to, *args, **options)
+rescue ErrorDuringExecution
+  # `curl` error 33: HTTP server doesn't seem to support byte ranges. Cannot resume.
+  if $CHILD_STATUS.exitstatus == 33 && continue_at == "-"
+    continue_at = "0"
+    retry
+  end
+
+  raise
 end
 
 def curl_output(*args, **options)