The 44-year-old rap star has taken aim at Pete, 28, on social media, posting a throwback snap of the comedian joking about his mental health struggles on 'Saturday Night Live'. Kanye West wants "payback" against Pete Davidson.
In the image, Pete - who is dating Kanye's estranged wife, Kim Kardashian - is seen wearing a cap that reads, "Make Kanye 2006 Again".
The skit also made fun of Kanye's friendship with former US President Donald Trump.
Kanye - who refers to Pete as "Skete" - wrote on Instagram: "HI SKETE YOU GOT ANYMORE MENTAL HEALTH JOKES FOR ME? (sic)"
In a follow-up post, Kanye also insisted his comments didn't amount to harassment.
He wrote online: "This boy thought he could get away with performing this sketch for the team that wrote this for him."
Kanye added: "This is not harassment This is payback. (sic)"
In the skit, Pete performed an impression of the rap star, who has North, eight, Saint, six, Chicago, four, and Psalm, two, with Kim.
The comedian said: "This is the real me. I am off the meds, take 'em, no shame in the medicine game."
Kanye - who has previously been diagnosed with bipolar disorder - recently apologised for "harassing" Kim on social media.
The 'Stronger' hitmaker deleted all of his recent posts about his estranged wife and said he was "learning in real time".
Alongside a photo of himself on stage, Kanye - who married the brunette beauty in 2014 - wrote: "I've learned that using all caps makes people feel like I'm screaming at them.
"I'm working on my communication. I can benefit from a team of creative professionals, organizers, mobilizers and community leaders. Thank everybody for supporting me. (sic)"