Multi-constraint trajectory planning method for unmanned aerial vehicles（UAVs）has been widely used in military and civil field, and trajectory solving method is an effective way to improve the efficiency of mission completion. In previous studies, the particle swarm optimization algorithm, which regards the UAV as a particle for trajectory planning, ignores the flight time, angle and other parameters of the UAV, and only contains position information. Aiming at the problem of UAV trajectory planning with fixed time and multiple constraints, a trajectory planning method based on particle swarm optimization and UAV kinematic model is proposed. Firstly, considering that the optimization of each control variable will cost a lot of time, the flight time of UAV is discretized as a certain number of Chebyshev points, they are the moments that the control variables are optimized, and can reduce the computational burden. On this basis, the angular velocity is taken as control variable, the function of angular velocity solved by curve fitting, and the function of angular and position of UAV is obtained by integration. The results are substituted into the particle swarm optimization model and combined with the UAV kinematic model to optimize the solution. Then, the angular velocity, angle and position are calculated according to the allocated time. Finally, the simulation of UAV trajectory planning in complex environment is carried out, and different situations are listed for compare and verification. In order to verify the effectiveness of the proposed method, Monte-Carlo simulation is used. Simulation shows that the proposed method can accurately calculate the kinematic parameters, plan a smooth trajectory and successfully avoid the obstacles in the process of forward. Besides the dimension of solution and feasibility of trajectory planning are improved effectively.