The zebra optimization algorithm is a brand-new optimization algorithm based on swarm intelligence. This algorithm has been successfully applied to solve many complex optimization problems. Although there are many improved algorithms based on the Zebra Optimization Algorithm, they all lack rigorous convergence analysis and cannot theoretically prove whether the algorithm can reach the global optimum. Therefore, the improved algorithms lack theoretical support. Therefore, the Markov theory in stochastic processes is utilized to conduct convergence analysis on the zebra optimization algorithm, laying a solid theoretical foundation for the improvement and engineering application of the zebra optimization algorithm. Firstly, the mathematical definitions of the zebra state space and the transition probability of the zebra position in the zebra optimization algorithm are given. Secondly, the Markov chain model of the zebra optimization algorithm is established. Then, it is demonstrated that the Markov chain of the zebra group state sequence is finite and homogeneous, and its state space is reducible. Finally, combined with the global convergence criterion of the algorithm, it is proved that the Markov chain model of the zebra optimization algorithm can meet the two assumptions of the global convergence of the random search algorithm, verifying the global convergence of the algorithm. In addition, numerical experiments on the zebra optimization algorithm are carried out by selecting 16 standard test functions with different characteristics. The correctness of the theoretical proof is successfully verified, and the characteristics of the zebra optimization algorithm are also demonstrated.