Trajectory planning is an important subject in the field of unmanned aerial vehicles (UAVs). However, existing methods do not solve some problems well, such as slow convergence speed and low searching efficiency of related algorithms and collisions between UAVs and the obstacles. Therefore, a method is proposed to solve a trajectory planning problem for multi-UAV in a static environment, which includes three main phases: the initial trajectory generation, the trajectory correction, and the smooth trajectory planning. First, the improved algorithm called MACO which introduces the metropolis criterion into the node screening mechanism of the ant colony optimization (ACO) algorithm is presented to generate the initial trajectory that can effectively avoid falling into the local optimal solution and stagnation. Then, considering size constraint of UAVs, this paper gives three trajectory correction schemes to solve the collision avoidance problem and further to optimize the initial trajectory. Last, the discontinuity originated from the sharp turn which occurred in the trajectory planning is solved by the inscribed circle (IC) smooth method, and the produced trajectory has shown better performance in reducing fuel consumption and improving the trajectory safety. Experimental results demonstrate that the proposed method has the high feasibility and effectiveness from aspects of the optimal solution, the collision avoidance, and the smooth trajectory in the trajectory planning problem for UAVs.