"Just tried watching Saturday Night Live - unwatchable! Totally biased, not funny and the Baldwin impersonation just can't get any worse. Sad," Mr Trump wrote.
Baldwin refused to let Mr Trump have the last word, tweeting back "@realDonaldTrump, release your tax returns and I'll stop. Ha."
Last week, Mr Trump also tweeted that he was displeased with the show.
However, last week, he waited until the following morning to share his views.
"Watched parts of @nbcsnl Saturday Night Live last night. It is a totally one-sided, biased show - nothing funny at all. Equal time for us?" Mr Trump wrote.
Baldwin told him to focus on something important rather than his displeasure at Saturday Night Live.
"Equal time? Election is over. There is no more equal time. Now u try 2 b Pres + ppl respond. That's pretty much it," Baldwin's first tweet read. "You know what I would do if I were Prez? I'd be focused on how to improve the lives of AS MANY AMERICANS AS POSSIBLE."