The group has won five Grammy Awards : Best Alternative Album for Dookie , Best Rock Album for American Idiot , Record of the Year for `` Boulevard of Broken Dreams '' , Best Rock Album for the second time for 21st Century Breakdown and Best Musical Show Album for American Idiot : The Original Broadway Cast Recording .
They also have won three Grammy Awards , Best Alternative Album for Dookie , Best Rock Album for American Idiot , and Record of the Year for the song `` Boulevard of Broken Dreams '' .