In　real-world　scenarios,　partial　information　losses　of　multivariate　time　series　degrade　the　time　series　analysis.　Hence,　the　time　series　imputation　technique　has　been　adopted　to　compensate　for　the　missing　values.　Existing　methods　focus　on　investigating　temporal　correlations,　cross-variable　correlations,　and　bidirectional　dynamics　of　time　series,　and　most　of　these　methods　rely　on　recurrent　neural　networks　(RNNs)　to　capture　temporal　dependency.　However,　the　RNN-based　models　suffer　from　the　common　problems　of　slow　speed　and　high　complexity　when　dealing　with　long-term　dependency.　While　some　self-attention-based　models　without　any　recurrent　structures　can　tackle　long-term　dependency　with　parallel　computing,　they　do　not　fully　learn　and　utilize　correlations　across　the　temporal　and　cross　variable　dimensions.　To　address　the　limitations　of　existing　methods,　we　propose　a　novel　so-called　dual-branch　cross-dimensional　self-attention-based　imputation　(DCSAI)　model　for　multivariate　time　series,　which　is　capable　of　performing　global　and　auxiliary　cross-dimensional　analyses　when　imputing　the　missing　values.　In　particular,　this　model　contains　masked　multi-head　self-attention-based　encoders　aligned　with　auxiliary　generators　to　obtain　global　and　auxiliary　correlations　in　two　dimensions,　and　these　correlations　are　then　combined　into　one　final　representation　through　three　weighted　combinations.　Extensive　experiments　are　presented　to　show　that　our　model　performs　better　than　other　state-of-the-art　benchmarkers　on　three　real-world　public　datasets　under　various　missing　rates.　Furthermore,　ablation　study　results　demonstrate　the　efficacy　of　each　component　of　the　model.(c)　2023　The　Authors.　Published　by　Elsevier　B.V.　This　is　an　open　access　article　under　the　CC　BY　license　(http://creativecommons.org/licenses/by/4.0/).