Random noise in seismic data affects the signal-to-noise ratio, obscures details, and complicates identification of useful information. We have developed a new method for reducing random, spike-like noise in seismic data. The method is based on a 1D stationary median filter (MF) — the 1D time-varying median filter (TVMF). We design a threshold value that controls the filter window according to characteristics of signal and random, spike-like noise. In view of the relationship between seismic data and the threshold value, we chose median filters with different time-varying filter windows to eliminate random, spike-like noise. When comparing our method with other common methods, e.g., the band-pass filter and stationary MF, we found that the TVMF strikes a balance between eliminating random noise and protecting useful information. We tested the feasibility of our method in reducing seismic random, spike-like noise, on a synthetic dataset. Results of applying the method to seismic land data from Texas demonstrated that the TVMF method is effective in practice.