Seismic waveform data are generally contaminated by noise from various sources. Suppressing this noise effectively so that the remaining signal of interest can be successfully exploited remains a fundamental problem for the seismological community. To date, the most common noise suppression methods have been based on frequency filtering. These methods, however, are less effective when the signal of interest and noise share similar frequency bands. Inspired by source separation studies in the field of music information retrieval (Jansson et al., 2017) and a recent study in seismology (Zhu et al., 2019), we implemented a seismic denoising method that uses a trained deep convolutional neural network (CNN) model to decompose an input waveform into a signal of interest and noise. In our approach, the CNN provides a signal mask and a noise mask for an input signal. The short‐time Fourier transform (STFT) of the estimated signal is obtained by multiplying the signal mask with the STFT of the input signal. To build and test the denoiser, we used carefully compiled signal and noise datasets of seismograms recorded by the University of Utah Seismograph Stations network. Results of test runs involving more than 9000 constructed waveforms suggest that on average the denoiser improves the signal‐to‐noise ratios (SNRs) by , and that most of the recovered signal waveforms have high similarity with respect to the target waveforms (average correlation coefficient of ) and suffer little distortion. Application to real data suggests that our denoiser achieves on average a factor of up to improvement in SNR over band‐pass filtering and can suppress many types of noise that band‐pass filtering cannot. For individual waveforms, the improvement can be as high as .