An apparatus and method are provided for compensating for a position error of a resolver that compensates for positions in the overall speed range using resolver position error measured at a specific speed by providing an angle tracking observer (ATO) for calculating angle information. The ATO compensates for the position errors in the overall speed range based on the position errors measured at the specific speed, to an inside of a resolver-digital converter. The method includes digitalizing detected position information of the motor rotor and receiving the digitalized position information from a resolver-digital converter to measure the position error. An electrical angular velocity of the position error is determined and the position error at the electrical angular velocity 0 is calculated and stored. The position error at a current electrical angular velocity is converted into and compensated for using the calculated position error based on the current electrical angular velocity.