We propose a method for hyperspectral image (HSI) super-resolution by designing a tensor singular value decomposition (t-SVD) and three-dimensional total variation (3D-TV) regularization terms. The super-resolution method is designed as an optimization problem whose cost function consists of a data-fidelity term, the low-rank representation term by t-SVD, and the 3D-TV regularization term. The sparse representation term is used to enhance the low-rank quality to unify the spectrum and space of HSI. Furthermore, the 3D-TV regularization term exploits the spectral and spatial similarity between adjacent pixels of HSI. Then we develop an effective algorithm for solving the resulting optimization by the alternative direction method of multipliers. The results on the simulated and the real data demonstrate that the proposed method is competitive with other state-of-the-art methods.