A vehicle control device which disengages a clutch provided in an automatic transmission when brake-off and accelerator-off are brought about during traveling of a vehicle and stops an engine and carries out inertia traveling, comprising: a determining unit configured to determine whether or not a brake pedal has been depressed; an accelerator pedal position detecting unit configured to detect an accelerator pedal position; and an accelerator pedal position change rate calculating unit configured to calculate temporal change rate of the accelerator pedal position; characterized in that it further comprises: an engine start control unit configured to select whether to start the engine by push-start by engaging the clutch and by transmitting power of the driving wheel to the engine or to start the engine using a starter motor based on a result of determination as to whether or not the brake pedal has been depressed and on the temporal change rate of the accelerator pedal position during the inertia traveling; wherein the engine start control unit starts the engine by the push-start by engaging the clutch and by transmitting the power of the driving wheel to the engine if the temporal change rate of the accelerator pedal position becomes a predetermined threshold value or more during the inertia traveling, and wherein the engine start control unit makes, when the engine is to be started by the push-start, an engagement speed of the clutch when it is determined by the determining unit that the brake pedal has been depressed slower than the engagement speed of the clutch when the temporal change rate of the accelerator pedal position is at the predetermined threshold value or more. a determining unit configured to determine whether or not a brake pedal has been depressed; an accelerator pedal position detecting unit configured to detect an accelerator pedal position; and an accelerator pedal position change rate calculating unit configured to calculate temporal change rate of the accelerator pedal position; characterized in that it further comprises: an engine start control unit configured to select whether to start the engine by push-start by engaging the clutch and by transmitting power of the driving wheel to the engine or to start the engine using a starter motor based on a result of determination as to whether or not the brake pedal has been depressed and on the temporal change rate of the accelerator pedal position during the inertia traveling; wherein the engine start control unit starts the engine by the push-start by engaging the clutch and by transmitting the power of the driving wheel to the engine if the temporal change rate of the accelerator pedal position becomes a predetermined threshold value or more during the inertia traveling, and wherein the engine start control unit makes, when the engine is to be started by the push-start, an engagement speed of the clutch when it is determined by the determining unit that the brake pedal has been depressed slower than the engagement speed of the clutch when the temporal change rate of the accelerator pedal position is at the predetermined threshold value or more. an engine start control unit configured to select whether to start the engine by push-start by engaging the clutch and by transmitting power of the driving wheel to the engine or to start the engine using a starter motor based on a result of determination as to whether or not the brake pedal has been depressed and on the temporal change rate of the accelerator pedal position during the inertia traveling; wherein the engine start control unit starts the engine by the push-start by engaging the clutch and by transmitting the power of the driving wheel to the engine if the temporal change rate of the accelerator pedal position becomes a predetermined threshold value or more during the inertia traveling, and wherein the engine start control unit makes, when the engine is to be started by the push-start, an engagement speed of the clutch when it is determined by the determining unit that the brake pedal has been depressed slower than the engagement speed of the clutch when the temporal change rate of the accelerator pedal position is at the predetermined threshold value or more.