Unmanned Aerial Vehicles (UAVs) play a crucial role in both military and civilian fields. As a key link in the practical application of UAV systems, it is of vital significance to study the algorithm of trajectory planning. The problem is set in a two-dimensional space based on the kinematic model of UAV. The trajectory planning in the study and the algorithm of the Rapid-exploring Random Tree (RRT), some improvement schemes, such as target orientation, bidirectional expansion, additional constraints and trajectory simplification are adopted to overcome some of its shortcomings such as low convergence efficiency, non-repeatability and absence of optimality. The significant effects of the improvement schemes are verified in the following simulation experiments. The comprehensive numerical simulation experiments of trajectory planning for single UAV and multiple UAVs are successfully conducted to verify the effectiveness and practicality of the algorithm of global trajectory planning based on improved RRT.