An engine start-up control device for a vehicle is provided with a structure which prevents the occurrence of an uncomfortable shock arising from amplified engine load torque fluctuation caused by resonance, when an output of a first motor generator starting up an engine by driving the same is limited. With a second motor generator having reactive torque restricting the rotation of a transfer member, the first motor generator rotatably drives a sun gear to crank the engine for start-up thereof. When this takes place, if the output of the first motor generator is limited, torque reference reactive-force control is executed to control reactive torque of the second motor generator in accordance with a predetermined torque whereby when the engine load torque exceeds a predetermined value, a rotation speed variation of the transfer member is permitted against reactive torque such that the rotation speed variation of the transfer member allows engine load torque to escape for thereby precluding engine load torque fluctuation to be amplified due to resonance.