Under the bill, an ounce or less of pot would result in a maximum $500 fine.
Right now, it could cost you up to $2,000 and up to 180 days in jail.
RELATED: Multiple bills aim to expand medical marijuana in Texas
If the bill passes the House, it goes to the Texas Senate.
In Harris County, people caught with less than four ounces of pot enter a diversion program. That's been in place since 2017.
Everything you need to know about Harris Co.'s pot policy