A bi-rotation Lyapunov vector fields based obstacle avoidance algorithm(BLBOAA) is proposed for unmanned aerial vehicles(UAVs). Firstly, the models of UAV and obstacle are established, and the decision rules of obstacle are established based on an assessment of whether UAV would rush into the safety circle within a finite time. Then, based on the principle of minimum lateral offset, the optimal obstacle avoidance direction is selected from rotation direction of UAV's velocity and its reverse direction is selected as vector field rotation direction. Then, criterion of successful obstacle avoidance is defined and proved. Finally, the established rule of obstacles combination improves the effecienty of obstacle avoidance, and BLBOAA is suitable for on-line obstacle avoidance under the uncertain environment. Simulation results show that the UAV can avoid the dynamic and static obstacles effectively under the dynamic constraint, and the performance of the proposed algorithm is better than that of the Dubins path and artificial potential field.