An oil pump driving control device of a vehicle having a main oil pump (14) that is driven by a motor/generator (4) and produces a pump discharge oil to a first clutch (3), , a second clutch (5) and a belt-type continuously variable transmission (6) provided on a driving force transmission line. A hybrid control module (81) is provided in this FF hybrid vehicle. The hybrid control module (81) is configured to perform a control so that during vehicle stop, the lower an ATF oil temperature is, the more the pump driving energy to drive the main oil pump (14) is decreased. With this control, consumption energy during the vehicle stop can be reduced.