A control apparatus of a vehicle that calculates a feedback requested acceleration for maintaining an inter-vehicle distance to a target distance and a feedforward requested acceleration for causing the own vehicle to travel following a communicating preceding vehicle and calculates a requested acceleration of the own vehicle on the basis of the feedback and feedforward requested accelerations. The apparatus executes a control that causes the own vehicle to travel following the preceding vehicle by controlling the acceleration of the own vehicle such that the acceleration of the own vehicle corresponds to the requested acceleration of the own vehicle. The apparatus sets the feedforward requested acceleration to zero when a shift lever of the preceding vehicle is positioned at a shift position other than a shift position that causes the preceding vehicle to travel forward and the feedforward requested acceleration is larger than zero.