This paper proposes a stock price prediction model based on a combination method of recurrent neural networks (RNN) and attention mechanisms. The goal is to improve the forecasting accuracy of financial time series data. By applying the attention mechanism to the RNN architecture, the model can learn dynamic importance weights for different time steps. This allows better capture of dominant features in stock price volatility. The study utilizes real Apple Inc.'s stock prices between January 2024 and January 2025 to build models and validate the models. Normalizing and implementing train-test strategies were used to preprocess data in a bid to enhance stability within the models. Experiments utilize mean squared error (MSE), mean absolute error (MAE), and the coefficient of determination (R2) as evaluation metrics for the model. Comparative evaluation was performed against a set of mainstream popular models. Results show that the constructed RNN+Attention model outperforms traditional RNN, LSTM, MLP, and Transformer models both in prediction accuracy and fitting performance. In addition, visualizations demonstrate a strong correspondence between predicted values and actual values. The curve of training loss shows a clear downward trend, further supporting the effectiveness and convergence of the model. This method provides an efficient and realistic technical solution to stock price prediction using deep learning.