An apparatus and method for detecting movement errors due to the wheel slip or transient current generated while a mobile robot is traveling. The movement error detecting method includes: detecting movement of the wheels in a sensor part according to a movement command input to a drive motor, and outputting an actual output value from the sensor part; calculating an ideal output value for output from the sensor part as the wheels are moved according to the movement command; and comparing the actual output value with the ideal output value to determine and residual fault and detect movement errors.