A method and system may detect a fail of a steering angle sensor in an electric power steering apparatus. The system may include: a steering angle sensor for generating and transmitting a steering angle signal measuring a rotation angle of a steering wheel; a motor for generating an assistant power for smooth steering and transmitting a current and a voltage based on rotation of the motor; and an Electronic Control Unit (ECU) for receiving the current and the voltage from the motor, sensing the rotation direction of the motor, receiving the steering angle signal from the steering angle sensor, sensing a first rotation direction of the steering wheel, and then, when the rotation direction of the motor is not equal to the first rotation direction of the steering wheel, determining that the steering angle signal has a fail and starting operation of a fail-safe logic.