Ultimate Fighting Championship

In June 2011, Papy signed a four-fight deal with the Ultimate Fighting Championship, and it was announced that he would drop down to welterweight for his UFC debut.^[5]

Abedi made his UFC debut against former title challenger Thiago Alves on November 5, 2011, at UFC 138.^[6] Abedi was badly hurt by a straight right hand from Alves that knocked him down midway through the first round and after delivering a barrage of punches and elbows that cut Abedi open, Alves took Abedi's back and finished the fight via submission due to a rear naked choke, giving Abedi his first professional loss. Although Abedi was given credit for stepping up against a top 10-fighter in his UFC debut.^[7]

Abedi faced James Head on April 14, 2012, at UFC on Fuel TV: Gustafsson vs. Silva.^[8] Late in the opening round Head stunned Abedi with a short elbow from the clinch followed by a barrage of punches that knocked Abedi down, Head followed Papy to the mat and finished the fight with a rear naked choke.^[9]

Abedi was briefly linked to a bout with Rick Story on June 22, 2012, at UFC on FX: Maynard vs. Guida, replacing an injured Rich Attonito^[10][11] However, Abedi was forced out of the bout with an injury and replaced by promotional newcomer Brock Jardine.^[12][13]

In his third fight with the promotion, Abedi faced fellow Swedish fighter Besam Yousef at UFC on Fuel TV 9.^[14] He won the back-and-forth fight via split decision, earning his first UFC win.^[15]

Abedi next faced Dylan Andrews in his return to middleweight on August 28, 2013, at UFC Fight Night 27.^[16] Despite controlling and winning the first two rounds, Abedi lost via knockout in the third round. After the loss Abedi was subsequently released from the UFC.^[17]

Post UFC

After his run in the UFC, Abedi went back to fight in Sweden. He was expected to face Daniel Acácio for the Superior Challenge welterweight title on May 3, 2014, at Superior Challenge 10,^[18] but pulled out with an injury and was subsequently replaced by Alan Carlos.^[19][20]

Abedi made his return, first expected at April 9, 2016 but later postponed, from what was an over three-year layoff, to face Bruno Carvalho in a middleweight bout on October 8, 2016, at Superior Challenge 14.^[21][22] He won the fight by TKO in the first round.^[23]

He faced Dylan Andrews, in a rematch of their 2013 UFC-bout, for the Superior Challenge Middleweight Championship on April 1, 2017, at Superior Challenge 15.^[24] He lost the fight by knockout via head kick in the 2nd round.^[25]