The House Regulated Industries Committee approved the measure Wednesday. A similar bill has already cleared a key Senate panel. Gov. Nathan Deal has said he'll sign the legislation.
The bill approved on Wednesday would allow communities to ask voters to decide if they want to allow Sunday sales after 12:30 p.m. It originally only permitted beer and wine sales but was amended to include liquor in areas that already permit the sale of spirits.
Georgia, Connecticut and Indiana are the only three states that ban the Sunday sale of alcohol at stores.
Previous efforts to allow Sunday alcohol sales in Georgia have stalled amid a veto threat from former Gov. Sonny Perdue.