The training required to receive a concealed-carry permit "doesn't teach how to respond emotionally and technically" to a school shooting situation, he said.
Lawmakers in states and in the nation's capital have called for new measures to combat gun violence in schools following the recent massacre at Sandy Hook Elementary School in Connecticut, where 20 children and six adults were fatally shot.
Dewhurst's proposal echoes the solution suggested last month by the National Rifle Association (NRA). NRA executive vice president Wayne LaPierre called for Congress to provide funding to establish armed guards in every public school.
Texas state law prohibits guns in schools, but individual school districts may waive that rule for school staffmembers.
It's unclear whether the lieutenant governor has submitted an actual proposal to the state legislature, but a similar bill, to allow concealed weapons in college classrooms, failed in 2011.