At the Grand Prix Final, Mura finished last in the short program and fourth in the free skate, ending fifth overall. He competed in the 2014–15 Japan Figure Skating Championships, where he finished 5th. When Tatsuki Machida retired from figure skating, Mura was named as his replacement to represent Japan at the 2015 World Figure Skating Championships, along with Yuzuru Hanyu and Takahiko Kozuka. He was also selected to represent Japan at the 2015 Four Continents Figure Skating Championships, where he finished seventh. At the World Championships, Mura finished in 16th place.