Rear-wheel steering system and controlling method thereof

The present disclosure relates to a rear-wheel steering system and a controlling method thereof. The rear-wheel steering system includes: a rack configured to transmit a driving force generated from arear-wheel steering motor to rear wheels; a first correction module configured to, when an engine is started, detect a position of the rack using a displacement sensor and calculate a first correction value that is a difference between the detected position and a neutral position; a second correction module configured to, when the engine is started, detect a position of the rack using a motor position sensor that detects a rotation angle of the rear-wheel steering motor and calculate a second correction value that is a difference between the detected position and the neutral position; a comparison determiner configured to compare the first correction value and the second correction value to determine whether the displacement sensor has malfunctioned; and a steering controller configured to control an operation of