Stock price forecasting plays an important role in supporting investment decision-making in volatile financial markets. This study compares the performance of Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) models in predicting the closing price of PT Bank Rakyat Indonesia (BBRI.JK) stock using daily closing price data from Yahoo Finance for the period November 2, 2020, to October 30, 2025. The research methodology includes data collection, preprocessing, model development, and evaluation. The results show that the GRU model outperforms LSTM in prediction accuracy, achieving an RMSE of 90.14, MAPE of 1.86%, and MAE of 68.89, while LSTM records an RMSE of 111.00, MAPE of 2.37%, and MAE of 87.55. In terms of computational efficiency, LSTM requires less training time (343.57 seconds) compared to GRU (471.98 seconds). The Diebold–Mariano test yields a DM statistic of 1.9949 with a p-value of 0.0461, indicating a statistically significant difference in predictive accuracy, where GRU produces lower prediction errors. This study provides empirical insights into the trade-off between accuracy and computational efficiency of deep learning models for stock price forecasting.