In the context of local shading affecting photovoltaic arrays, the traditional maximum power point tracking algorithms exhibit slow convergence, poor accuracy, significant power fluctuations, and a susceptibility to getting trapped in local optima. For this reason, a composite algorithm based on the combination of a novel adaptive cuckoo algorithm and particle swarm algorithm was proposed. The method introduced adaptive discovery probability and adaptive L-vy flight step control factor into the cuckoo algorithm, and also incorporated the opposing population strategy in order to improve the algorithm′s convergence speed and global optimization seeking ability. In the early stage of the algorithm, the global search with particle swarm algorithm was used to quickly find the vicinity of global maximum power point (GMPP), and in the later stage, the new adaptive cuckoo algorithm was used to accurately search for the optimization in the local range in order to quickly, accurately, and stably track to the global maximum power point. The simulation results show that the convergence time and tracking error of the algorithm proposed in this paper are 0.106 s and 0.012%, 0.108 s and 0.034%, 0.110 s and 0.059%, and 0.106 s and 0.031%, respectively, for the four lighting modes, which are better than the other algorithms, and it validates that the algorithm in this paper has the fastest convergence speed, highest tracking accuracy, minimal power fluctuations, and the least likelihood of getting trapped in local optima among the six compared algorithms.