A∗ algorithm [1], [2] is a commonly used path planning method and it traditionally does search on the grid map. This results in discontinuous path and it does not consider the starting and final vehicle pose when planning. We propose a modified version, called Dubins-path-based A∗ algorithm, for a fixed-wing unmanned aerial vehicle (UAV) with obstacles avoidance. Assume the vehicle flies on a constant altitude without sideslip. Path searching will be applied on a weighted graph constructed by Dubins path. Simulations are provided to verify that the safe and flyable path can be generated by this method. Analysis shows it takes advantage over the commonly used A∗ algorithm applied on a grid map in aspects of the optimality and efficiency.