Owing to its advantages in acquisition properties, distributed acoustic sensing (DAS) is gradually being applied in seismic exploration. Unfortunately, the acquired DAS records are usually contaminated by various unwanted interferences, which are considered one of the main obstacles for subsequent processing, such as inversion and imaging of the seismic data. In general, conventional signal processing methods cannot satisfy the requirements of DAS noise attenuation owing to the limitations in presumption and denoising accuracy. Therefore, deep learning, especially convolutional neural networks (CNNs), has been used to eliminate intense background noise and improve the quality of DAS records. Nevertheless, most CNN-based methods often rely on single-scale features and cannot guarantee denoising performance when dealing with complex DAS data. In this study, we develop a multistage residual network (MSR-Net) aiming to enhance denoising ability for complex DAS background noise. More precisely, the backbone of MSR-Net adopts a multiscale architecture to capture informative features within the DAS data. A modified ringed residual module is also used to enhance the representation ability of potential features. In addition, a feature aggregation spatial attention module is designed to refine and reinforce the primary features, thereby positively impacting the denoising performance. Meanwhile, an authentic training data set is generated based on field noise data and synthetic records obtained by the forward-modeling method. Compared with conventional methods and typical denoising networks, MSR-Net demonstrates superiority in weak signal recovery and intense DAS noise attenuation.