In the process of recording terahertz digital hologram, the hologram is easy to be contaminated by speckle noise, which leads to lower resolution in imaging system and affects the reconstruction results seriously. Thus, the study of filtering algorithms applicable for de-speckling terahertz digital holography image has important practical values. In this paper, non-local means filtering and guided bilateral filtering were brought to process the real image reconstructed from continuous-wave terahertz coaxial digital hologram. For comparison, median filtering, bilateral filtering, and robust bilateral filtering, were introduced as conventional methods to denoise the real image. Then, all the denoising results were evaluated. The comparison indicates that the guided bilateral filter manifests the optimal denoising effect for the terahertz digital holography image, both significantly suppressing speckle noise, and effectively preserving the useful information on the reconstructed image.