The 27-year-old is up for best female vocalist and best entertainer and is nominated twice in the video of the year category, reports the BBC.
The awards will be handed out at a Las Vegas ceremony on 3 April.
Lambert will be competing with Swift, Keith Urban, Jason Aldean, Toby Keith and Brad Paisley for the top prize.
Lambert's fiance, Blake Shelton, is nominated in two categories, including male vocalist of the year. (ANI)