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.　(C)　2020　SPIE　and　IS&T