In this paper, the novel optimization model for tensor completion by considering the bi-level optimization model with the smooth $\epsilon$-trace functions instead of nuclear norm is proposed. In the new model, it is not necessary to perform singular value decomposition for all modes of the tensor in each iteration, but only two singular value decomposition is needed at most, which effectively reduces the huge computation amount brought by all modes expansion of the tensor and greatly improves the computation efficiency. Finally, the experimental results of randomly generated tensor completion problem and color image inpainting problem show that the proposed bi-level (minimin and minimax combination) optimization models usually has less than CPU time and better precision than the traditional nuclear norm based model.