With the increasing complexity of power grid data, traditional load forecasting methods have gradually revealed their limitations. To address this, this study introduces a method combining the Firefly Optimization Algorithm (FOA) with Recurrent Neural Networks (RNN) to improve the prediction accuracy and stability of the model. Through experimental comparisons of FOA-RNN with traditional RNN, SVM-NN, and GA-RNN algorithms, the results show that FOA-RNN performs excellently across multiple evaluation metrics. In terms of Mean Squared Error (MSE), FOA-RNN achieves a value of 0.0135, significantly lower than other models. The Mean Absolute Error (MAE) is 0.0957, much lower than RNN’s 0.1512, demonstrating FOA-RNN’s advantage in reducing prediction errors. Additionally, FOA-RNN’s Weighted Mean Squared Error (WMSE) is 0.0108, and its training loss is 0.0054, indicating superior training stability and convergence speed compared to other algorithms. In conclusion, the FOA-RNN model exhibits high accuracy, stability, and convergence efficiency in power grid load forecasting tasks, providing strong decision-making support for power grid scheduling and management. However, the model’s computational complexity remains high, and further optimization is needed to improve its real-time applicability.