The invention relates to a gas pressure regulator (1) for regulating the pressure of a gaseous fuel, said gas pressure regulator having a housing (2) in which a gas piston (3) movable longitudinally is arranged ), the gas piston delimits a gas chamber (5) and delimits a pressure chamber (7) that can be filled with a working fluid, wherein the gas piston (3) has a first seal (24) surrounding its outer side, The gas piston (3) is guided sealingly on the housing (2) by means of the first seal and the first seal seals the gas chamber (5). The cooperation of the gas piston (3) and the valve seat (21) forms an overflow valve (20), via which gas can be led out of the gas chamber (5). A second circumferential seal (25) is formed on the outside of the gas piston (3), by means of which the gas piston (3) is likewise guided in a sealing manner in the housing (2) , wherein the gas piston (3) is at least partially surrounded by a low-pressure gas chamber (9), and the second seal (25) separates the low-pressure gas chamber (9) from the gas return chamber (10) , wherein the gas chamber (5) can be connected to the gas return chamber (10) through the overflow valve (20). The invention also relates to a system for supplying an internal combustion engine with gaseous fuel, the system having an intermediate tank (200) and such a gas pressure regulator (1). Furthermore, in a method for operating the system there is a return accumulator ( 300 ), the pressure of which is set between the pressure in the gas chamber ( 5 ) and the pressure in the gas tank ( 100 ).