State Rep. Trey Martinez Fischer is pushing a bill that would force Taser users to apply for one with the Department of Public Safety, qualify and then take a training course.
Those convicted of a felony would be ineligible to apply.
"If a felon got one, he'd just go around zapping people and robbing people. It wouldn't be good at all," East El Paso resident Tom Crowell said.
Lawmakers hope to have the bill passed by the end of session next May.
Personal Tasers go on sale next April.