Permanent magnet arc motor (PMAM) has gained increasing prominence in the industrial applications. To enhance the motor performance of PMAM, the surrogate modeling and optimal design are necessary work. Aim at addressing the work, this paper proposes a new surrogate modeling and optimal design method for a PMAM based on the Deep Forest and Bayesian optimization algorithm (BOA). First, the motor structure of the PMAM is presented. Then, a simplified analytical model is developed to identify the structural parameters and design objectives. The finite element (FE) model of the PMAM is built to acquire sample data. To heel, a new Shapley Additive Explanations-based parameter importance evaluation method is introduced to evaluate the importance of structural parameters to design objectives. Subsequently, a new and accurate surrogate modeling method based on the Deep Forest is proposed to model the functional correlation between design objectives and structural parameters. After that, the powerful BOA is employed to search for the optimal structural parameters, enhancing the PMAM’s motor performance. Finally, the FE simulation and prototype experiments of the PMAM are conducted to validate the proposed design method.