A fuel gas supply system comprising: a storage tank for receiving liquefied gas and boil-off gas; a first fuel gas supply line provided with a compression unit pressurizing boil-off gas of the storage tank and supplying boil-off gas pressurized through the compression unit to a first engine; a second fuel gas supply line branched from an intermediate portion of the compression unit and supplying boil-off gas partially pressurized by the compression unit to a second engine; and a re-liquefaction line for receiving and re-liquefying a part of the pressurized boil-off gas, wherein the re-liquefaction line comprises a cooling unit for cooling the pressurized boil-off gas, a first expansion valve for primarily depressurizing the pressurized boil-off gas that has passed through the cooling unit, a first gas-liquid separator for separating boil-off gas which has passed through the first expansion valve and is in a gas-liquid mixed state into gas components and liquid components, a boil-off gas circulation line for supplying the gas components separated in the first gas-liquid separator to the second engine, and a liquefied gas circulation line for receiving the liquid components separated in the first gas-liquid separator, characterized in that the fuel gas supply system further comprises a heating value regulator for measuring and regulating a heating value of fuel gas supplied to the second engine, wherein the heating value regulator comprises a heating value measuring device for measuring a heating value of the fuel gas supplied to the second engine, and a first flow rate regulation valve provided at the second fuel gas supply line and a second flow rate regulation valve provided at the boil-off gas circulation line. a storage tank for receiving liquefied gas and boil-off gas; a first fuel gas supply line provided with a compression unit pressurizing boil-off gas of the storage tank and supplying boil-off gas pressurized through the compression unit to a first engine; a second fuel gas supply line branched from an intermediate portion of the compression unit and supplying boil-off gas partially pressurized by the compression unit to a second engine; and a re-liquefaction line for receiving and re-liquefying a part of the pressurized boil-off gas, wherein the re-liquefaction line comprises a cooling unit for cooling the pressurized boil-off gas, a first expansion valve for primarily depressurizing the pressurized boil-off gas that has passed through the cooling unit, a first gas-liquid separator for separating boil-off gas which has passed through the first expansion valve and is in a gas-liquid mixed state into gas components and liquid components, a boil-off gas circulation line for supplying the gas components separated in the first gas-liquid separator to the second engine, and a liquefied gas circulation line for receiving the liquid components separated in the first gas-liquid separator, characterized in that the fuel gas supply system further comprises a heating value regulator for measuring and regulating a heating value of fuel gas supplied to the second engine, wherein the heating value regulator comprises a heating value measuring device for measuring a heating value of the fuel gas supplied to the second engine, and a first flow rate regulation valve provided at the second fuel gas supply line and a second flow rate regulation valve provided at the boil-off gas circulation line.