Under the same geological conditions, the thickness and length of the reinforced strip, the slope ratio of the reinforced embankment, the modulus of elasticity of the fill and the reinforced strip, and the friction angle at the interface between the reinforcement and the soil, are the main design parameters that have an important influence on the stress, deformation, and stability of the encompassing reinforced soil embankment. To quickly and accurately determine the optimal design parameters for reinforced soil embankments with wrapped faces, ensuring minimal cost, while maintaining structural safety, we propose a design parameter prediction model based on a GA–BP neural network. This model evaluates parameters within their specified ranges, using maximum lateral displacement, maximum vertical displacement, maximum stress in the XZ direction, the maximum shear strain increment, and the safety factor, as assessment criteria. The primary objective is to minimize the overall cost of the embankment. A comparison with five machine learning algorithms shows that the model has high prediction accuracy, and the optimal design parameter combinations obtained from the optimization search can significantly reduce the cost of the embankment, while controlling the displacement and stability of the embankment. Therefore, the GA–BP network is suitable for predicting the optimal design parameters of reinforced soil embankments with wrapped faces.