In this talk, we present a novel tensor completion model which combines the laplace function and an anisotropic total variation regularization. The laplace function is utilized to approximate the tensor multi-rank, and the total variation regularization is added to improve the local piecewise smoothness and preserve the edges of the restored tensor data. An efficient alternating direction method of multipliers is proposed to tackle the tensor completion model, and its convergence theorem is also derived. Extensive experimental results on color images, videos, multispectral images and magnetic resonance imaging data show the efficiency and effectiveness of the proposed method.