A working-fluid supply system configured to supply working fluid to a fluid apparatus, the working-fluid supply system comprising: a first pump configured to be driven by output from a first driving source, the first pump being capable of supplying the working fluid to the fluid apparatus; a second pump configured to be driven by output from the first driving source, the second pump being capable of supplying the working fluid to the fluid apparatus; a first switching valve capable of switching a supply target of the working fluid from the second pump to either one of a discharge side of the first pump and a suction side of the first pump; a first switching control unit configured to perform a switching control of the first switching valve in accordance with a required flow amount of the working fluid required by the fluid apparatus; and a first pressure control unit (25, 47) configured to perform a control such that pressure on the suction side of the first pump becomes a predetermined first pressure when the first switching valve is switched such that the supply target of the working fluid from the second pump becomes the suction side of the first pump, characterized in that the first pressure control unit (25, 47) has: a second switching valve provided on a returning flow passage (20, 23) connecting the first switching valve with the suction side of the first pump, the second switching valve being capable of switching the supply target of the working fluid from the second pump to either one of the suction side of the first pump and a tank in which the working fluid is stored; and a second switching control unit configured to switch the second switching valve such that the supply target of the working fluid from the second pump becomes the suction side of the first pump in a case in which the pressure on the suction side of the first pump is equal to or lower than the first pressure, the second switching control unit being configured to switch the second switching valve such that the supply target of the working fluid from the second pump becomes the tank in a case in which the pressure on the suction side of the first pump is higher than the first pressure. a first pump configured to be driven by output from a first driving source, the first pump being capable of supplying the working fluid to the fluid apparatus; a second pump configured to be driven by output from the first driving source, the second pump being capable of supplying the working fluid to the fluid apparatus; a first switching valve capable of switching a supply target of the working fluid from the second pump to either one of a discharge side of the first pump and a suction side of the first pump; a first switching control unit configured to perform a switching control of the first switching valve in accordance with a required flow amount of the working fluid required by the fluid apparatus; and a first pressure control unit (25, 47) configured to perform a control such that pressure on the suction side of the first pump becomes a predetermined first pressure when the first switching valve is switched such that the supply target of the working fluid from the second pump becomes the suction side of the first pump, a second switching valve provided on a returning flow passage (20, 23) connecting the first switching valve with the suction side of the first pump, the second switching valve being capable of switching the supply target of the working fluid from the second pump to either one of the suction side of the first pump and a tank in which the working fluid is stored; and a second switching control unit configured to switch the second switching valve such that the supply target of the working fluid from the second pump becomes the suction side of the first pump in a case in which the pressure on the suction side of the first pump is equal to or lower than the first pressure, the second switching control unit being configured to switch the second switching valve such that the supply target of the working fluid from the second pump becomes the tank in a case in which the pressure on the suction side of the first pump is higher than the first pressure.