In this paper, a disturbance observer (DOB) approach is developed to reject disturbance and achieve precision position control of a quadcopter. The Q-filter is tuned to deal with both drift and noise from the onboard sensors. The position estimates are obtained from a hybrid low-pass and de-trending (HLPD) filter. Simulation and experimental flight tests are conducted to demonstrate the performance of the proposed control technique. Experimental flight tests, which include hover test and waypoint following test, prove that the performance of the proposed algorithm is better than the widely used cascaded PID-PID structure. The algorithm doesn't rely on a motion capture system for position estimates which makes it suitable for outdoor flight missions.