Tensor completion recovers missing entries of multiway data. Most of the current methods exploit the low-rank tensor structure for image completion applications. In this paper, we simultaneously exploit the globally multidimensional structure and locally piecewise smoothness to further enhance the performance. In the proposed optimization model, the low tensor tree rank minimization is used for the global data structure, and the total variation minimization is used for the local structure. Two kinds of total variation functions are discussed. The optimization problem is transformed into several subproblems by alternating direction method of multipliers. The subproblem on low tensor tree rank minimization is solved by singular value thresholding, and the subproblem on total variation minimization can be solved by soft thresholding. Numerical experiments on color images and light field images demonstrate that the proposed method outperforms most of the state-of-the-art methods in terms of recovery accuracy and computational complexity.