NOVELTY - An on-board fuel cell system comprises a main passage connecting a hydrogen gas storage device with an inlet of a fuel cell; a circulation passage connecting an outlet of the fuel cell with a first point in the main passage; a pump in the circulation passage; and a bypass passage connecting a second point between the outlet of storage device and first point.    USE - On-board fuel cell system for use on a motor vehicle, e.g. automobile.    ADVANTAGE - The on-board fuel cell system is lightweight and compact in size for installation on a vehicle. It assures a high degree of safety.    DETAILED DESCRIPTION - An on-board fuel cell system comprises a hydrogen gas storage device (200) including a hydrogen gas-absorbing alloy capable of absorbing or releasing a hydrogen gas. A fuel cell (100) is supplied with the hydrogen gas discharged from the hydrogen gas storage device to generate electric power while discharging a remaining portion of the hydrogen gas. A first passage (401) connects an outlet of the hydrogen gas storage device with an inlet of the fuel cell and allows the hydrogen gas discharged from the hydrogen gas storage device to flow to the fuel cell. A second passage (403) connects an outlet of the fuel cell with a first point in the first passage and allows the hydrogen gas discharged from the fuel cell to be returned to the first passage. A pump (410) in the second passage forces the hydrogen gas in the second passage to flow toward the first point in the first passage. A third passage (405) connects a second point located in the first passage between an outlet of the hydrogen gas storage device and the first point. A third point is located in the second passage between the outlet of the fuel cell and the pump. The third passage allows the hydrogen gas diverting from the first passage to be fed to the second passage. A first valve (202) in the first passage between the second point and the first point is able to permit and inhibit flow of gas upon opening and closing, respectively. A second valve in the second passage between the outlet of the fuel cell and the third point is able to permit and inhibit flow of gas upon opening and closing, respectively. A third valve in the third passage is able to permit and inhibit flow of gas upon opening and closing, respectively. A controller controls the pump and the valves. When a pressure of the hydrogen gas discharged from the storage device is higher than a reference pressure, the controller opens the first and second valves and closes the third valve so that the hydrogen gas discharged from the storage device is supplied to the fuel cell through the fist passage. The hydrogen gas discharged from the fuel cell is returned to the first passage through the second passage with the pump circulating the hydrogen gas. When the pressure of the hydrogen gas discharged from the storage device is lower than the reference pressure, the controller closes the first and second valves and opens the third valve and causes the pump to draw the hydrogen gas out of the storage device and feed the hydrogen gas from the first passage to the second passage through the third passage so that the hydrogen gas is supplied from the second passage to the fuel cell through the first passage.    An INDEPENDENT CLAIM is included for a method of controlling an on-board fuel cell system by determining whether the pressure of the hydrogen gas discharged from the storage device is higher than a reference pressure and opening the first and second valves and closing the third valves or determining whether a pressure of the hydrogen gas discharged from the storage device is lower than a reference pressure and closing the first and second valves while opening the third valve.    DESCRIPTION OF DRAWING(S) - The figure shows a construction of an on-board fuel cell system as above.    Fuel cell (100)    Storage device (200)    First valve (202)    First passage (401)    Second passage (403)    Third passage (405)    Gas-liquid separator (406)    Fourth passage (409)    Pump (410)    Relief valve (416)