Real-time monitoring of urban high-altitude data is an important goal in the construction and development of smart cities today. However, with the development of modern cities, the monitoring space becomes complicated and narrow because of the different building heights and no-fly zones, which makes UAV trajectory planning more difficult. In this paper, a multi-strategy sparrow search algorithm (MSSA) is proposed to solve the UAV trajectory planning problem in a three-dimensional environment. The algorithm aims to minimize the flight distance and maximize the use efficiency of the UAV. First, the improved algorithm employed a reverse-learning strategy based on the law of refraction to improve the search range and enhance the optimization performance. Second, we introduced a random step size generated by Levy flight into the position update strategy of the participant. The algorithm accuracy and speed of convergence were improved by the randomness feature. Finally, the algorithm incorporated the Cauchy mutation to improve the scout position, which enhanced its ability to jump out of the local optimum of the algorithm. Sixteen benchmark test functions, Wilcoxon rank sum test, and 30 CEC2014 test function optimization results demonstrated that MSSA had better optimization accuracy, convergence speed, and robustness than the comparison algorithms. In addition, the proposed algorithm was applied to the UAV trajectory planning problem in different complex 3D environments. The results confirmed that the MSSA outperformed the other algorithms in complex 3D trajectory planning problems.