Because of the extremely low signal-to-noise ratio of pulsar signals, it is difficult to suppress noise while preserving details by the traditional denoise methods. Therefore, a wavelet domain pulsar signal denoising method based on a differentiable thresholding function and an adaptive threshold selection technique is presented. The signal-to-noise ratio(SNR), the root mean square error(RMSE), the relative error of the peak value (REPV) and the error of the peak position (EPP) are used to evaluate the performance of the proposed denoising method. Experimental results show that the proposed method can remove the pulsar signal noise and keep the useful information effectively. At the same time, it can achieve a higher PSNR, a lower RMSE, a lower REPV and a lower EPP than the soft thresholding and hard thresholding methods.