Uncertain factors such as manufacturing error, assembly error and operational wear will cause the dimension deviation of the optimal structural parameters for permanent magnet synchronous linear motor (PMSLM), which will result in the deterioration of the thrust performance for PMSLM. A robust optimization method based on interval-mind evolutionary algorithm back propagation (I-MEABP) neural network is proposed in this paper. First, the analysis model of thrust performance for PMSLM is established, and the key structural parameters that have greater impacts on the thrust performance of PMSLM are obtained. Second, the I-MEABP neural network is formed to establish the robust numerical model of thrust performance for PMSLM based on the key structural parameters. It integrates the interval analysis theory into the Mind Evolutionary Algorithm Back Propagation (MEABP) neural network and a robust modeling method I-MEABP is formed. It can take the interval structural parameters that include structural dimension deviations as input variables and takes the interval thrust performance values as output values based on the interval sample library. Third, the adaptive whale optimization algorithm (AWOA) is applied to optimize the robust model, and the robust optimal interval values of structural parameters are obtained. Compared with the deterministic optimization method, the robustness of the results in this paper is higher; compared with other robust methods, this robust method obtains the optimal interval of structural parameters for PMSLM, which is different from the optimal point. Finally, Finite element analysis and motor prototype experiments prove the robustness and superiority of the proposed method.