Strangely I can't download 7.16.21 for Mac. Every attempt is refused as failed.
I don't know how to update my version 7.16.19.
Please help me to solve this problem.

Do you mean it won't download from this link or it won't install once you download it? I don't have a Mac but it downloads fine for me.

Yes it doesn't download anything from the link you mentioned. I've a copy of it and when I start it gives a message "The application “BOINC Installer.app” can’t be opened.".

The link that Dave provided downloads a single file called "boinc_7.16.21_macOSX_universal.zip" - the '.zip' indicates that it's a compressed archive file, containing all the real moving parts.

Macs should be able to "extract all..." - that's the Windows terminology, but the Mac should be similar. Inside, there's another folder called "boinc_7.16.21_macOSX_universal" (no extension). And inside that, there's a document titled "ReadMe.rtf". That's your starting point.