Thanks to the multi-linearity nature of data, tensor completion approaches often achieve significantly improved performance than matrix based techniques. These methods mostly use the Tucker model and need to frequently compute the singular value decompositions (SVD) of unfolding matrices, hence are not qualified for large-scale data. In this paper, a randomized tensor completion method is proposed to solve this problem. In the proposed method, efficient orthogonal random projection is employed to take the place of SVD, which significantly reduce the computational complexity. Extensive experimental results on color image recovery applications showed that the proposed method is considerably faster than state-of-the-art while achieving comparable peak signal-to-noise ratio.