Capacity analysis of satellite network, especially multilayer one, is of theoretical and practical significance for improving the network efficiency and strengthening the guaranteed ability of network services. However, existing solutions, which usually focus on Up/Down links (UDLs) of satellite network, without considering the characteristics of satellite network, e.g., dynamic topology, limited resources, periodicity, are not scalable for the capacity analysis of Inter-Satellite links (ISLs) of Multi-Layer Satellite Network (MLSN). In this paper, we present a capacity analysis method for MLSN based on an improved Distributed Genetic Algorithm (DGA). The improved DGA, as an intelligent optimization algorithm, is used to solve the problems of network capacity analysis. Moreover, the capacity analysis method is applied in the MLSN to analyze the network capacity and extensively evaluated. Simulation results demonstrate that the method can efficiently calculate the upper bound and lower bound of network capacity with faster convergence speed, higher searching precision and ability of avoiding premature convergence. In addition, we conclude that node failures lead to the decrease of network capacity and different constellation structures have different effects on the upper bound and lower bound of network capacity.