But it's unclear whether Brown, a gun owner who has not taken an official position, will sign the "open-carry" bill, which would make California the first state since 1987 to outlaw publicly displaying a weapon, the Los Angeles Times reported.
The bill, passed by the Legislature last week, would make public display of an unloaded weapon a crime carrying up to a year in jail and a $1,000 fine.
"Open carry puts law enforcement and families at risk on Main Street, California," said Assemblyman Anthony Portantino, D-La Canada Flintridge, who proposed the measure. He said the practice also wastes time when law enforcement officers deal with calls about people openly carrying weapons in coffee shops, restaurants and malls.
Los Angeles County Sheriff Lee Baca, the California Police Chiefs Association and Los Angeles Police Chief Charlie Beck also said they support the measure.
"We need to limit the number of guns in public, not increase them by wearing them on our hips," Beck said. "This is not Dodge City. … We are a modern civilized community, and we should work on peaceful solutions to end criminal behavior."
The measure would not affect citizens' right to carry concealed weapons if they have a permit.
Open-carry supporters say public display of unloaded guns poses no risk.
"There is no reason to (ban the practice) other than a general dislike of gun rights," said John Pierce, a spokesman for OpenCarry.org.