In general, an oil pump driving control device for a hybrid vehicle is described. A hybrid vehicle includes a drive-train configured and arranged to transmit power in the order of an engine, a first clutch, a motor generator, a second clutch and a drive wheel, and an oil pump operably configured and arranged at a location between the first clutch and the second clutch such that the oil pump is mechanically driven by at least one of the engine and the motor generator. The invention provides an oil pump driving control device that supplies the necessary oil pressure for an automatic transmission with only a single mechanical oil pump. For example, even when it is not possible to maintain tightening of the second clutch, oil pressure may be supplied by rotating the oil pump using the motor generator. In this way, the oil pressure may be supplied with a single oil pump.