A control apparatus is applied to a system including an engine and a compressor for air-conditioning, and adjusts an operating point of the engine when the engine is operated. The control apparatus determines whether or not to allow increase in engine output to drive a compressor based on an air-conditioning request, based on the operating point of the engine before driving of the compressor in relation to a predetermined high-efficiency region including a maximum efficiency point in an efficiency characteristics of the engine, when the compressor is driven in response to the air-conditioning request. The control apparatus controls the engine output such that the operating point of the engine is in the high-efficiency region, if the increase in engine output is determined to be allowed.