West, who is known for his epil Twitter meltdowns, said Ezrin, best known for his work with musicians Lou Reed, Alice Cooper, Kiss and Pink Floyd, was a nobody.
Ezrin, 66, had said that unlike other musicians of his generation it would be unlikely that West's songs will be quoted 20 years from now.
"Kanye's greatest achievements have been in the form of excessive behavior, egomaniacal tantrums and tasteless grandstanding," Ezrin wrote.
"Has anybody ever heard of Bob Ezrin???" West, 38, began his series of tweets.
"I'm tired of old people that have no connection with anything trying to comment on music!. Do something relevant... Please don't speak on me bro ever again!!! Bro you said Macklemore was more important musically than me... No offense to Macklemore, he's a nice human being!," West tweeted.
The tweets are tame compared to his earlier outbursts but West did go after Ezrin's children.
The rapper also referred to his ongoing feud with Swift, who he had earlier made up after his 2009 mic grab from Swift at VMAs.
Although he didn't specifically refer to the two-time album of the year Grammy winner, West seemingly put it out there. "I made Dark Fantasy and Watch the Throne in one year and wasn't nominated for either and you know who has 2 albums of the year," he tweeted.
