A wiper control apparatus includes a wiper motor for operating a wiper, and providing a ground terminal, a low-speed terminal, and a high-speed terminal. A cam plate is disposed inside the wiper motor and generates a control signal for stopping the wiper when an operation mode of the wiper is a stop mode. A controller is configured to selectively supply a power to a low-speed terminal and a high-speed terminal of the wiper motor by turning on/off of a low-speed relay and a high-speed relay according to an operation mode of the wiper, to selectively turn off the low-speed relay and the high-speed relay by using the control signal according to a rotation of the cam plate, and to decelerate a wiper speed when the wiper stops.