With the development of Maritime Autonomous Surface Ships (MASSs), the mission success assessment problem cannot be ignored because of potential security issues of MASSs. This paper addresses the issue of performance degradation at different stages, the problem of state dependence in multi-stage missions of MASSs, and the correlation problem between missions of stages. Based on the coupling of the reliability model of each single-stage mission system, a multi-stage mission success evaluation method for MASSs is proposed. By leveraging the ability of the conditional probability tables in Bayesian networks to express the complex relationships between the nodes, the dynamic Bayesian network model of stages is constructed based on the fault tree. Based on the Markov process, the problem of state dependence on shared equipment between stages is solved. Considering the complex relationship between multi-stage missions, the virtual node is introduced, and the multi-state Bayesian network is combined to realize the coupling of the reliability evaluation results of each single-stage mission. It is applied to the multi-stage mission success evaluation of the MASS to obtain the success probability of MASSs and the key equipment of each stage. The results show that evaluation results are more suitable for engineering practice.