"You are a rude, terrible person. You shouldn't be working for CNN," Trump said.
"The way you treat Sarah Huckabee Sanders is horrible," he said, referring to his press secretary. "And the way you treat other people is horrible."
Acosta wasn't the only reporter with whom the President sparred. The next questioner, NBC reporter Peter Alexander, defended his CNN colleague as a fine reporter.
"Well, I'm not a big fan of yours, either, honestly," Trump told Alexander. "Just sit down please," he said to Acosta.
"When you report fake news, which CNN does a lot, you are the enemy of the people," Trump said.
Later, he criticized PBS reporter Yamiche Alcindor for asking a "racist question".
Alcindor, who is black, asked whether Trump thought his declaration during the campaign that he's a "nationalist" had emboldened white supremacists who call themselves "white nationalists".
"Such a racist question," Trump complained, adding that he found it "insulting".
- Bloomberg