Higher-order Singular Value Decomposition (HOSVD) for tensor decomposition is widely used in multi-variate data analysis, and has shown applications in several areas in computer vision in the last decade. Conventional multi-linear assumption in HOSVD is not translation invariant - translation in different tensor modes can yield different decomposition results. The translation is difficult to remove as preprocessing when the tensor data has missing data entries. In this paper we propose a more general multi-affine model by adding appropriate constant terms in the multi-linear model. The multi-affine model can be computed by generalizing the HOSVD algorithm; the model performs better for filling in missing values in data tensor during model training, as well as for reconstructing missing values in new mode vectors during model testing, on both synthetic and real data.