An accurate and efficient surrogate model plays a significant role in the optimal design of electrical motors. This article presents an accurate and efficient surrogate modeling method for a flux reversal permanent magnet arc motor (FR-PMAM) based on machine learning algorithm. Specifically, the motor topology and the optimized design of the FR-PMAM are firstly illustrated. Then, the PM magnetic motive force-permeance model is developed to select structural parameters of FR-PMAM. After that, a finite-element analysis (FEA) model of FR-PMAM is calculated to obtain sample data. A machine learning algorithm random forest is introduced into the field of motor optimal design for the first time to evaluate the contribution of each parameter to the design objectives. Based on the sample data, an efficient machine learning algorithm CatBoost is innovatively employed to establish the accurate and efficient surrogate model of the FR-PMAM that can capture the complex function relationship between output objectives and input parameters. Subsequently, an improved genetic algorithm with the elitist reservation strategy is adopted to obtain the optimal combination of the structural parameters of FR-PMAM. Finally, a prototype of the FR-PMAM is manufactured. The FEA and experimental results validate the effectiveness of the investigated surrogate modeling method.