This paper addresses the position sensorless control for brushless DC motor (BDCM) with repetitive positiondependent load torque which is a function of the absolute rotor position (not incremental rotor position). The robust sensorless control is composed of sensorless control and robust speed control. In order to commutate winding currents, the former one estimates the incremental rotor positions from the motor terminal voltages without any position sensor. In order to reduce the speed variations due to position-dependent load, a robust speed control is developed without estimating the absolute rotor position and other system parameter. In this paper, the effects of position-dependent load on the speed variations and the commutation intervals are studied in first. It shows that the position-dependent load can be estimated from the commutation intervals. Then, we develop the position sensorless control based on sensing terminal voltage from sensorless circuit and the robust speed control with adaptive gain. Finally, some simulated results have been given to demonstrate the robust performance of the proposed sensorless control for the position-dependent loads.