A gas engine heat pump and a method of operating the same are provided. According to an embodiment of the present disclosure, the gas engine heat pump includes: an engine for burning a mixture of air and fuel; an exhaust gas compressor for compressing exhaust gases coming from the engine; a buffer tank for storing the exhaust gases compressed by the exhaust gas compressor; an exhaust gas valve disposed between the buffer tank and an intake manifold of the engine; an exhaust gas spray nozzle for spraying the exhaust gases stored in the buffer tank into a cylinder of the engine; an exhaust gas sensor for acquiring information on the exhaust gases coming from the engine; and a controller, wherein the controller controls the operation of at least one of the exhaust gas valve and the exhaust gas spray nozzle, based on the information on the exhaust gases acquired by the exhaust gas sensor. Other various embodiments are possible.