An apparatus for controlling rear wheel steering includes a steering angle sensor detecting a steering angle of a steering wheel; a vehicle speed sensor detecting a vehicle speed of a vehicle; a steering torque sensor detecting a steering torque applied to a steering shaft; and a control unit calculating a front wheel angle and a steering angle velocity from the steering angle detected by the steering angle sensor, calculating a rear wheel angle compensation factor for improving rear wheel steering responsiveness based on at least one of the steering torque detected by the steering torque sensor and the calculated steering angle velocity and a same/opposite phase gain depending on the vehicle speed detected by the vehicle speed sensor, and calculating a target rear wheel angle based on the front wheel angle, the rear wheel angle compensation factor and the same/opposite phase gain.