The advancements in speech recognition have led to significant progress in predicting clean speech. However, challenges persist in real-world noisy environments. Addressing issues such as speech distortion and noise residue in signals processed by speech enhancement models, we propose a noise-robust speech recognition method based on the Dual-Path Gated Spectral Refinement Network (DGSRN). We construct a single-channel speech enhancement model based on dense time-frequency convolutional networks for the first stage of noise suppression. And the Dual-Path Gated Spectral Refinement Network is designed to extract useful features from estimated noise to enhance speech quality. Multi-task joint training is conducted using a weighted speech distortion loss function. Experimental results demonstrate that compared to traditional joint training approaches, DGSRN achieves a 12.41% reduction in Character Error Rate, addressing the issue of mismatched performance on evaluation metrics.