In order to improve the prediction accuracy of foundation pit deformation, an improved exponential power product (EPP) foundation pit deformation prediction model was proposed based on the improved whale optimization algorithm with Laplace crossover operator (LXWOA). First, the simulation results of the LXWOA were verified by four standard test functions, and compared with those of basic whale optimization algorithm (WOA), gray wolf optimization (GWO) algorithm, sine cosine algorithm (SCA) and particle swarm optimization (PSO) algorithm. Then LXWOA was used to optimize the exponential parameters of the EPP model, by which the LXWOA-EPP deformation prediction model was constructed. Meanwhile, the WOA-EPP, GWO-EPP, SCA-EPP, PSO-EPP models were constructed to compare with the LXWOA-SVM and LXWOA-BP models. The case study data of a foundation pit mentioned in a paper was used in the models for verification purposes. The delay time and the embedding dimension of the models were determined by auto-correlation function method and false nearest neighbor method respectively to construct the input and output vectors, and then the first 15 and last three sets of the pit monitoring data were used to train the models for better prediction outcomes. The results show that the search ability of LXWOA is better than that of WOA, GWO, SCA and PSO algorithms, and it has better optimization precision and global search ability. The absolute relative error, mean absolute error and root mean square error of the foundation pit predicted by LXWOA-EPP model are 0.18%, 0.008 mm, and 0.009 mm, respectively, which are better than the six models of WOA-EPP and literature records. This indicates that the parameters of EPP models can be effectively optimized by LXWOA, and the LXWOA-EPP model is applicable and effective for deformation predictions. This model and method can provide some reference for other related prediction studies.