When applied to the design of high-gain high-bandwidth orbital-angular-momentum (OAM) antennas loaded by substrates, the full-wave analysis suffers from drawbacks such as low efficiency and extended period for parameter scanning. We propose a surrogate model based on a back propagation neural network (BPNN) to improve the efficiency of parameter scanning and the design process. Compared to the traditional single-objective surrogate model for the return loss function, the proposed BPNN-based model is a multi-objective surrogate model for a simplified S-matrix ignoring mutual coupling effects between non-adjacent antenna elements. During the establishment process, the surrogate model must undergo multiple iterations of genetic algorithm (GA) optimization and calibration through full-wave analysis, with mean absolute percentage errors (MAPE) being the calibration standard. After employing it in a dielectric-loaded uniform circular array of six rectangular patches, the design based on the surrogate model can significantly reduce training time and the MAPE by less than 2.5%. The method can accelerate the construction of dielectric-loaded planar antenna arrays for various applications in communication systems.