A device for compensating friction of a motor driven power steering system, comprising a sensing unit for sensing at least one of a steering angle, an angular speed and a vehicle speed, and a steering torque corresponding to the at least one of the steering angle, the angular speed and the vehicle speed; and a control unit for storing the steering torques sensed through the sensing unit in a storage unit when the at least one of the steering angle, the angular speed and the vehicle speed sensed through the sensing unit falls into the respective setting range. The control unit calculates an average value of the stored steering torques when the number of steering torques stored in the storage unit is equal to or higher than a reference number, and computes a friction-compensating torque based on a result obtained by comparing the average value with a reference value.