The Safe Schools Improvement Act, of which Grimm is a cosponsor, would require public schools to create policies that prevent bullying and harassment.
"It's time that we all say enough is enough," Grimm said on the House floor Wednesday. "We must demand accountability from those charged with addressing bullying in our schools ... we owe it to all of our young adults."
Grimm had threatened to throw a reporter off a Capitol balcony after President Barack Obama's State of the Union address in January, though he admitted he "screwed up" after the incident.
In April, Grimm was indicted on 20 counts of fraud for allegedly evading taxes while running a Manhattan restaurant.
Grimm will face former New York City Councilman Domenic Recchia (D) in his Staten Island and Brooklyn district this November.