Disclosed are a control system and a control method for fail safety of a motor driven power steering (MDPS). The system may include a straight motion/turning determination module for determining whether a vehicle is in a straight motion or turning based on a steering angle of a steering wheel, a steering torque of the steering wheel and a vehicle speed of the vehicle, a fail determination module for determining whether an MDPS fail occurs based on a steering torque of a driver and a motor torque of the MDPS if the vehicle is in the straight motion, a fail type determination module for determining a type of the MDPS fail using a yaw rate change rate if the MDPS fail occurs, and a yaw rate change rate detection module for inputting the yaw rate change rate to the fail type determination module.