This study proposes a Grey Wolf Optimization (GWO) variant named Elastic Grey Wolf Optimization algorithm (EGWO) with shrinking, resilient surrounding, and weighted candidate mechanisms. Then, the proposed EGWO is used to optimize the weights and biases of Multi-Layer Perception (MLP), and the EGWO-MLP model for predicting student achievement is thus obtained. The training and verification of the EGWO-MLP prediction model are conducted based on the thirty attributes from the University of California (UCI) Machine Learning Repository dataset’s student performance dataset, including family features and personal characteristics. For the Mathematics (Mat.) subject achievement prediction, the EGWO-MLP model outperforms one model’s prediction accuracy, and the standard deviation possesses the stable ability to predict student achievement. And for the Portuguese (Por.) subject, the EGWO-MLP outperforms three models’ Mathematics (Mat.) subject achievement prediction through the training process and takes first place through the testing process. The results show that the EGWO-MLP model has made fewer test errors, indicating that EGWO can effectively feedback weights and biases due to the strong exploration and local stagnation avoidance. And the EGWO-MLP model is feasible for predicting student achievement. The study can provide reference for improving school teaching programs and enhancing teachers’ teaching quality and students’ learning effect.