An all-purpose gas stove structure capable of increasing its air intake includes an all-purpose opening-covering case, an extended supporting frame, and at least one gas nozzle. The all-purpose opening-covering case includes an opening-covering case body for covering the heat source-receiving opening of a roasting/grilling device completely, and a gas controller with a gas operation unit for controlling the state of communication between gas input and output ends. The extended supporting frame is a box with a protective lid, is coupled to the inner side of the opening-covering case body at one end, and has a stove burner opening at the opposite end. The lateral walls of the protective lid are formed with vent holes. The gas nozzle is provided on the inner side of the stove burner opening. The all-purpose gas stove structure allows a ceramic roasting/grilling device to have a higher air intake and therefore produce higher heat.