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Swarm intelligence algorithm is an emerging optimization method, which connects simple individuals through teamwork and organization to generate swarm intelligence and is used to solve practical problems. So far, there are many kinds of swarm intelligence algorithms. Cuckoo search (CS) is one of the typical swarm intelligence algorithms. It has the characteristics of simple implementation and high efficiency. In this paper, based on the principle of CS algorithm, a Markov chain model is constructed, its properties are analyzed, and the global convergence criterion is combined to prove the global convergence of CS algorithm. The experiment is simulated in two aspects: firstly, in the case of solving the same problem, this paper analyzes the complexity of 5 algorithms; secondly, 18 standard test functions are adopted to perform statistics on the 5 algorithms respectively. Under low and high dimension, the accuracy, convergence speed and stability of the 5 kinds of algorithms are compared. The experimental results show that cuckoo algorithm is of low complexity, and compared with other algorithms, it has high accuracy and good stability.