An apparatus and a method for controlling shifting of a vehicle are provided. The apparatus includes a transmission configured to transmit power generated from by a motor to a vehicle wheel, and a controller configured to control an operation of the transmission. The controller is configured to enter a LURCH control mode when sensing shifting of a shift lever between a D range and an R range during driving to maintain a clutch torque in the transmission, to decrease a vehicle speed by controlling a motor speed, and to shift a gear of the vehicle by changing a motor torque when the vehicle speed reaches a threshold speed.