A suitable trajectory in a port inspection mission is important for unmanned aerial vehicles (UAVs). Motion planning can help UAVs quickly generate an optimal trajectory that meets the constraints. The motion planning of UAVs is achieved in this paper as follows: firstly, a collision detection (CD) function is applied that evaluates whether the bias_RRT* (rapidly exploring random tree) algorithm needs to be called. Secondly, an isosceles triangle optimization function optimizes the path. Next, a trajectory is generated based on the minimum snap trajectory method. Lastly, the bias_RRT* algorithm and the improved bias_RRT* algorithm are used in the two experimental scenes for path planning comparison, and trajectory planning is carried out. The results show that, in the improved method, the path length and calculation time are shortened, and the trajectory cost and trajectory deviation are also significantly reduced. Overall, it appears that a camera-equipped UAV under the proposed approach can accomplish monitoring tasks more effectively and safety in port environment.