"I want to say to all the young women out there, there are going to be people along the way who will try to undercut your success, or take credit for your accomplishments or your fame," she said.
"But if you just focus on the work and you don't let those people sidetrack you, someday when you get where you were going, you'll look around and you will know that it was you and the people who love you that put you there. And that will be the greatest feeling in the world. Thank you, for this moment."
Swift beat out the Alabama Shakes, Kendrick Lamar, Chris Stapleton and The Weeknd for her prize.
Swift and West have had "bad blood," so to speak, since the 2009 MTV Music Awards in a moment that immediately went viral. A fired-up West interrupted Swift as she accepted the award for Best Female Video for "You Belong With Me" to declare that Beyonce had "one of the best videos of all time."