County Executive Rob Astorino said it would be inappropriate for the county to hold the event.
Former County Executive Andrew Spano had banned the show after the 1999 Columbine school shootings in Colorado. The ban remained in effect for more than a decade.
Astorino brought back the show in 2010.
His decision comes after Greenburgh Town Supervisor Paul Feiner called on the county to cancel the show at the government-owned building.
Westchester Board of Legislators Chairman Ken Jenkins said banning such shows at the County Center was part of the answer to curbing gun violence.
The show's promoter, Westchester Collectors, didn't return respond to calls for comment.
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