The 25-year-old 'Blank Space' hitmaker has also received nods in categories including Best Collaboration and Best Female Performance.
Lamar is nominated in the same category for his own "Alright".
Other names vying for the award are Ed Sheeran ("Thinking Out Loud"), Beyonce Knowles ("7/11") and Mark Ronson ("Uptown Funk" featuring Bruno Mars).
In addition to the Video of the Year title, Swift's "Bad Blood" clip is up for a bunch of other awards like Best Collaboration, Best Visual Effects, Best Art Direction, Best Editing and Best Cinematography. Its director Joseph Kahn is eyeing the Best Direction trophy.
The former two are pitted against each other for Best Male Video and Best Pop Video.
The latter, meanwhile, also has her "7/11" in contention for Best Female Video and Best Choreography among others.
The 2015 Video Music Awards is airing live on MTV on August 30. Miley Cyrus has announced that she's hosting the event.
"MTV won't let me perform... So I'm hosting this year's VMAs," she said on Monday.
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