A gas engine heat pump is provided including an engine having an ignition plug, a compressor connected to the engine, a mixer that mixes air and fuel and supplies the mixture to the engine, a zero governor having a valve that regulates the fuel supplied to the mixer, a throttle valve disposed between the mixer and the engine to regulate a flow of the mixture to the engine, and a controller. Upon receiving a command to stop running the engine, the controller changes a target number of revolutions of the engine, controls an opening degree of the valve based on the target number of revolutions if a current number of revolutions of the engine exceeds a first reference number, and controls the ignition plug to stop igniting if the current number of revolutions of the engine reaches a second reference number which is lower than the first reference number.