Inaccurate phase estimation in single-channel speech enhancement tasks will cause poor quality of the enhanced speech. To this end, this study proposes a speech enhancement method based on a deep complex axial self-attention convolutional recurrent network (DCACRN), which enhances speech amplitude information and phase information in the complex domain simultaneously. Firstly, a complex convolutional network-based encoder is employed to extract complex features from the input speech signal, and a convolutional hopping module is introduced to map the features into a high-dimensional space for feature fusion, which enhances the information interaction and the gradient flow. Then an encoder-decoder structure based on the axial self-attention mechanism is designed to enhance the model’s timing modeling ability and feature extraction ability. Finally, the reconstruction of the speech signals is realized by the decoder, while the hybrid loss function is adopted to optimize the network model to improve the quality of enhanced speech signals. Meanwhile, the mixed loss function is utilized to optimize the network model and improve the quality of enhanced speech signals. The experiments are conducted on the public datasets Valentini and DNS Challenge, and the results show that the proposed method improves both the perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) metrics compared to other models. In the non-reverberant dataset, PESQ is improved by 12.8% over DCTCRN and 3.9% over DCCRN, which validates the effectiveness of the proposed model in speech enhancement tasks.