In a gas engine system, air fed through a turbocharger is mixed with fuel gas flowing through a fuel gas supply line and supply into a combustion chamber is controlled. In case that the fuel gas has a low calorie or the engine output power is high, a portion of the fuel gas is diverged from the fuel gas supply line, and the flow rate thereof is set to a constant rate less than that of the diverged side fuel gas. The diverging fuel gas is fed into the combustion chamber through a divergence control valve while the remainder of the fuel gas is fed into the fuel flow control valve. In case that the fuel gas has a high calorie or the engine output power is low, the divergence control valve is closed so as to feed the fuel gas only into the gas supply main pipe.