The present disclosure relates to a gas engine heat pump including: an engine which burns a mixed air of air and fuel; a first exhaust flow path which is connected to the engine so that exhaust gas discharged from the engine passes through and is discharged to the outside; a turbo charger including: a first compressor which compresses the mixed air and supplies to the engine, and a first turbine which is installed in the first exhaust flow path and receives the exhaust gas passing through the first exhaust flow path to drive the first compressor; a supercharger which is installed in the first exhaust flow path between the engine and the first turbine, and receives and compresses the exhaust gas passing through the first exhaust flow path to supply to the first turbine; a second exhaust flow path which is branched from the first exhaust flow path between the engine and the supercharger, and converges to the first exhaust flow path between the supercharger and the first turbine; a first valve which is installed to be opened and closed in the second exhaust flow path; a third exhaust flow path which is branched from the first exhaust flow path between the supercharger and the first turbine, and converges to the first exhaust flow path in downstream of the first turbine; a second valve which is installed to be opened and closed in the third exhaust flow path; and a controller which controls operations of the first valve, the second valve, and the supercharger according to load of the engine.