Image smoothing is a prerequisite for subsequent operations in image processing. There are several techniques for image smoothing among which diffusion tensor smoothing is preferred in imaging the brain, muscles, heart, tumour and cancer cells. Data acquisition and transmission introduce impulse noise along with the ever present Gaussian noise. Image smoothing filters such as the mean filter, anisotropic diffusion filter, the bilateral filter and the guided filter are not intrinsically robust to impulse noise. They require additional complex structures for robustness. The robustness of diffusion tensor smoother has not been well studied. A statistical model for diffusion tensor image smoother is proposed consistent with the model for the standard anisotropic diffusion smoother. An algorithm is derived. The performance of the diffusion tensor smoother is investigated qualitatively and quantitatively. The intrinsic robustness of the diffusion tensor smoother and the superior performance thereof in comparison with the anisotropic diffusion are demonstrated.