In this paper, we aim at the completion problem of high order tensor data\nwith missing entries. The existing tensor factorization and completion methods\nsuffer from the curse of dimensionality when the order of tensor N>>3. To\novercome this problem, we propose an efficient algorithm called TT-WOPT\n(Tensor-train Weighted OPTimization) to find the latent core tensors of tensor\ndata and recover the missing entries. Tensor-train decomposition, which has the\npowerful representation ability with linear scalability to tensor order, is\nemployed in our algorithm. The experimental results on synthetic data and\nnatural image completion demonstrate that our method significantly outperforms\nthe other related methods. Especially when the missing rate of data is very\nhigh, e.g., 85% to 99%, our algorithm can achieve much better performance than\nother state-of-the-art algorithms.\n