In a hybrid vehicle equipped with an engine and a motor that are connected to a driveshaft linked to an axle via a gear mechanism, on condition that a torque demand Tr* required for the driveshaft is lower than a preset reference torque level Tref (step S220) and that a vehicle speed V is lower than a preset reference speed level Vref (step S230), the drive control of the invention idles the engine (step S240) regardless of a stop request of the engine (steps S120 and S210). This arrangement effectively reduces the potential for backlash or gear rattle in the gear mechanism. On condition that the vehicle speed V is not lower than the preset reference speed level Vref (step S220), on the other hand, the drive control of the invention stops the operation of the engine (step S250) in response to the stop request of the engine (steps S120 and S210) even under the torque demand Tr* of lower than the preset reference torque level Tref (step S230). This arrangement desirably enhances the energy efficiency of the hybrid vehicle.