A gas flow valve having pneumatic vibration dampening device to reduce the vibrations created by the flow of gas through the gas valve. The gas valve includes a gas flow conduit that terminates at a discharge opening. A valve member is movably positioned relative to the discharge opening and allows gas flow in a flow condition and prevents the flow of gas in a seated position. The valve member includes a gas passage formed within the valve member. At least one flexible membrane is mounted to the valve member and surrounds an outlet opening of the gas passage. The flexible membrane is inflated as the flow of gas within the gas flow conduit increases such that the flexible membrane contacts an inner surface of a stabilizing conduit. The interaction between the flexible membrane and the stabilizing conduit reduces the vibrations created by the flow of gas past the valve member.