A gas heat pump system is disclosed. The gas heat pump system includes an air conditioning module including a compressor, an outdoor heat exchanger, an expansion device, an indoor heat exchanger and a refrigerant pipe, an engine module including an engine configured to burn a mixture of fuel and air and provide power for operation of the compressor, a cooling module including a cooling water pump configured to generate flow of cooling water for cooling the engine and a cooling water pipe connected to the cooling water pump to guide flow of cooling water. The engine module includes a mixer configured to discharge the mixture of air and fuel to the engine, a supercharger disposed between the mixer and the engine to compress the mixture discharged from the mixer and discharge the mixture to the engine, and an adjuster disposed between the supercharger and the engine to adjust an amount of compressed mixture supplied to the engine.