Seismic prospecting is a common method used in oil and gas resource exploration. However, due to the limitations of current collection techniques, seismic records acquired in the field are typically contaminated by severe incoherent noise, which has negative implications for the subsequent processing and interpretation procedures. In addition, numerous traditional denoising algorithms have been applied in order to mitigate this problem, but further improvements are required, especially for the seismic data with spectral overlapping between effective signals and background noise. In recent years, feedforward denoising convolutional neural networks (DnCNNs) have been applied to suppress the complex random noise, and a series of essential insights have been gained. Nonetheless, conventional denoising networks always extract data features depending on single-scale information, resulting in impaired performance when coping with seismic records with a low signal-to-noise ratio (SNR). For solving this problem, a novel multiscale DnCNN (MSDCNN) is developed as an attempt for random noise suppression. Unlike conventional DnCNN, MSDCNN has a hierarchical structure capable of extracting features at different scales and capturing informative and discriminatory features through effective information integration. Meanwhile, the cross-scale feature interaction also increases the processing accuracy when confronted with weak reflection events. Experimental results derived from both synthetic and field data indicate that the proposed network can effectively suppress the random noise and accurately preserve reflection events, even under low SNR conditions.