This paper proposes a path planning algorithm called guiding attraction based random tree (GART), which is built upon the famous sampling-based algorithm RRT* to generate a near optimal path in real time for unmanned aerial vehicle (UAV) navigation under uncertainty. The algorithm takes UAV heading dynamic constraint and `obstacle safe attraction’ into consideration, and uses a descriptive set method to describe the uncertainty caused by control and sensing error. The analysis shows that the computational complexity of GART is within a constant factor of RRT* and RRT. A number of detailed comparisons of the proposed algorithm with RRT* in 2D are given which verify the efficiency of our algorithm. Moreover, 3D simulation results demonstrate that GART find the near optimal path only after 2400 iterations, which means that GART outperformed RRT* by 833%.