With the rapid development of artificial neural networks, more sophisticated network models and more accurate prediction results are provided for solving engineering applications. In this paper, the weights and thresholds of the feedforward neural network model were optimized using the pelican algorithm, and the optimal solution was output by simulating the pelican predation scheme and assigned as the new parameters of the neural network. A POA-BP network model was proposed, and its better prediction was demonstrated by comparing the fitting and prediction performance with 13 neural network models such as random forest, support vector machine, and wavelet basis by evaluating metrics such as RMSE, MSE, and MAE. To further improve the prediction accuracy, different hidden layer topologies of POA-BP were compared, and the Monte Carlo method was used to obtain seven design variables for the lithium battery shell size parameters, and parameter regression prediction was performed for the structure after the variable density topology optimization used the isotropic material interpolation model (SIMP) with the moving asymptote method by invoking the MinGW-w64 compiler, and the 1-3-1 neural network was selected model to predict each dimension of the battery shell structure, the final shell weight reduction ratio was 18.12% and the first-order intrinsic frequency was increased by 14.56%.