The Oil and Gas Production Rate (OGPR) is one of the most significant processes that play an essential role in the oil industry. Predicting OGPR is critical for effective reservoir management and enhancing oil recovery. Traditional methods (TMs) and numerical simulations (NS) often struggle to process and analyze nonlinear, complex, and massive datasets. To avoid these challenges, artificial intelligence (AI) techniques and machine learning (ML) models have been proposed as an alternative solution due to their high efficiency and rapidity in handling complex data. In this study, a new hybrid model is developed by combining the strengths of Artificial Neural Networks (ANN) and Gradient Boosting (GB), using Linear Regression (LR) as a meta-model by stacking technique. It captures nonlinear relationships effectively and manages outliers, enhancing prediction accuracy. The novelty of this study lies in the hybrid ANN-GB-LR model's ability to integrate various machine learning techniques into a robust framework, leveraging the high learning capacity of ANN, the robust handling of outliers by GB, and the straightforward interpretability of LR. This creative combination handles the limitations of individual models and enhances the general predictive performance. The model was trained and tested using actual field data from the Halewah field in Yemen. Evaluation metrics, including Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R-squared (R2), were utilized to evaluate and compare the hybrid model with other ML models: Random Forest (RF), XGBoost (XGB), LR, Light Gradient Boosting Machine (LGBM), GB, and K-nearest neighbors (KNN). The hybrid ANN-GB-LR model achieved superior results, with an R2 of 0.998, an RMSE of 11.06 for oil flow rate predictions, and an R2 of 0.98 and an RMSE of 172.15 for gas flow rate predictions. These results significantly surpass the other models, demonstrating the hybrid model's outstanding ability to capture complex data and provide accurate predictions. The ANN-GB-LR model surpasses Traditional Methods in predicting OGPRs. It shows a strong and reliable tool for optimizing reservoir management. This study establishes a new standard for predictive modeling in the oil industry, providing a framework for future research to apply hybrid models in handling complex datasets.