A fuel supply system for a hydrogen gas engine, having a metal hydride tank in which pellets or powders of a metal hydride absorbing and storing alloy are stored. A heat exchange device is arranged in the tank in contact with the metal hydride therein. The heat exchange device is connected to a heating medium source, such as an engine water jacket, for supplying the heating medium to the heat exchange device, for separating hydrogen gas from the metal hydride. A fuel supply conduit is provided for connecting the metal hydride tank with the engine. A hydrogen gas flow control valve and a hydrogen gas flow meter are arranged in series in the conduit. A controller is provided for controlling the hydrogen gas flow control valve so that a desired amount of the hydrogen gas, as detected by the hydrogen gas flow meter, is obtained. A sub tank may be provided for storing an excess amount of hydrogen gas from the main tank, which is introduced into the engine via a sonic valve. An indicator for measuring an amount of hydrogen gas remaining, from the volume of the metal hydride, is also provided.