A fuel gas supply apparatus comprising: a pressure-increasing means control unit that is arranged to control the discharge pressure of a pressure-increasing means for increasing the pressure of fuel gas to be supplied to a gas fired diesel engine; a main pipe that is arranged to guide the fuel gas whose pressure is increased by the pressure-increasing means to the gas fired diesel engine; pressure measurement means that is provided in the main pipe for measuring the pressure of the fuel gas to be supplied to the gas fired diesel engine; and a pressure adjustment valve that is provided on the upstream side of the pressure measurement means in the main pipe to adjust the pressure of the fuel gas whose pressure is increased by the pressure-increasing means to a set pressure (P1set) according to the load of the gas fired diesel engine; differential pressure measurement means for measuring a differential pressure before and after the pressure adjustment valve; a branch pipe that branches from the main pipe at an upstream position with respect to the pressure adjustment valve; and a buffer tank that is connected with the branch pipe and is arranged to absorb a variable pressure of the fuel gas in the main pipe caused by the pressure-increasing means, wherein the pressure-increasing means control unit is arranged to control the discharge pressure of the pressure-increasing means so that the differential pressure obtained by the differential pressure measurement means is increased when the pressure obtained by the pressure measurement means or the set pressure (P1set) is low and the differential pressure obtained by the differential pressure measurement means is decreased when the pressure obtained by the pressure measurement means or the set pressure (P1set) is high. a pressure-increasing means control unit that is arranged to control the discharge pressure of a pressure-increasing means for increasing the pressure of fuel gas to be supplied to a gas fired diesel engine; a main pipe that is arranged to guide the fuel gas whose pressure is increased by the pressure-increasing means to the gas fired diesel engine; pressure measurement means that is provided in the main pipe for measuring the pressure of the fuel gas to be supplied to the gas fired diesel engine; and a pressure adjustment valve that is provided on the upstream side of the pressure measurement means in the main pipe to adjust the pressure of the fuel gas whose pressure is increased by the pressure-increasing means to a set pressure (P1set) according to the load of the gas fired diesel engine; differential pressure measurement means for measuring a differential pressure before and after the pressure adjustment valve; a branch pipe that branches from the main pipe at an upstream position with respect to the pressure adjustment valve; and a buffer tank that is connected with the branch pipe and is arranged to absorb a variable pressure of the fuel gas in the main pipe caused by the pressure-increasing means, wherein the pressure-increasing means control unit is arranged to control the discharge pressure of the pressure-increasing means so that the differential pressure obtained by the differential pressure measurement means is increased when the pressure obtained by the pressure measurement means or the set pressure (P1set) is low and the differential pressure obtained by the differential pressure measurement means is decreased when the pressure obtained by the pressure measurement means or the set pressure (P1set) is high.