This study proposes DWT-FGRU, a stock price prediction model that combines Forget Gate Recurrent Unit (FGRU)—a modified GRU variant—with Discrete Wavelet Transform (DWT) to enhance modeling of financial time series. The FGRU improves upon the standard GRU by introducing a forget gate to filter irrelevant past information and by reconsidering the input to re-extract important features more effectively. Meanwhile, DWT performs multi-scale decomposition to reduce high-frequency noise, enabling clearer feature extraction and more stable learning. This dual mechanism allows the model to better capture both short-term fluctuations and long-term dependencies in volatile market data. Experiments on two stocks show that, on average, DWT-FGRU reduces Mean Squared Error by 85.7% for one-day forecasts and 84.9% for three-day forecasts compared to the standard GRU. These results demonstrate the model’s superior accuracy, robustness, and practical value, offering reliable forecasts to guide short- and medium-term investment strategies and risk management in live markets.