Attenuation of noise is a persistent problem in seismic exploration． The authors use conventional de- noising method to remove noise which may cause vibration near the discontinuity called pseudo- Gibbs artifact． In order to remove the artifact，the study proposed a method combining the seislet transform and total variation minimization． Firstly，the data are converted into the seislet transform domain． Secondly，the hard threshold was used for eliminating the noise and keep useful signal，which is the initial input for the next step． Finally， total variation minimization dealed with denoised data to recover boundary information and further eliminated the noise． Synthetic data examples show that the method has feasibility in eliminating random noise and protecting detailed signal，and also shows better results than the classic f- x deconvolution． The field data example also shows effective in practice． It can remove the noise and preserve the discontinuity signal at the same time．