The 77-year-old made the gaffe as he spoke to supporters during an I Will Vote Concert virtual event alongside his wife Jill.
“What kind of country we’re gonna be? Four more years of George, ah, George…,” he said before Mrs Biden corrected him under her breath.
Quickly rectifying himself, he continued: “Gonna find ourselves in a position where if Trump gets elected we’re going to be in a different world.”
Mr Trump was quick to call his opponent out on Monday morning following the apparent slip-up.
“Joe Biden called me George yesterday. Couldn’t remember my name. Got some help from the anchor to get him through the interview. The Fake News Cartel is working overtime to cover it up!” he tweeted.
Republicans have been keeping a close eye on any verbal mistakes by Mr Biden and have accused him of going senile.
A Trump campaign Twitter account, Trump War Room, which is often retweeted by the president, clipped up the video of the latest gaffe and shared it online.
Read more: sky news