Multi-modal　time　series　data　in　real　applications　often　contain　data　of　different　dimensionalities,　e.g.,　high-dimensional　modality　such　as　image　data　series,　and　low-dimensional　univariate　time　series.　Multi-modal　time　series　data　with　missing　high-dimensional　modal　values　are　ubiquitous　in　real-world　classification　and　regression　applications.　To　accurately　predict　the　target　labels,　it　is　important　to　appropriately　impute　the　high-dimensional　modal　missing　values.　However,　most　existing　imputation　methods　focus　on　multivariate　time　series,　fail　to　simultaneously　consider　temporal　dependencies　within　each　series　and　the　correlations　across　the　series,　and　also　lack　a　probabilistic　interpretation.　In　this　paper,　we　propose　a　novel　method,　which　uses　a　new　structured　variational　approximation　technique　for　the　imputation　of　missing　values　in　multi-modal　time　series.　Instead　of　directly　imputing　high-dimensional　modal　missing　values,　we　use　the　variational　approximation　technique　to　impute　intermediate　lower-dimensional　feature　representations　of　high-dimensional　modal　missing　values　from　simple　modalities　related　to　high-dimensional　modality　and　then　feed　them　into　a　dynamical　model.　The　dynamical　model　captures　the　temporal　dependencies　of　the　feature　representations　and　finally　predicts　the　target　labels.　In　order　to　address　the　optimization　difficulties　caused　by　the　lack　of　ground　truth　values　of　lower-dimensional　feature　representations,　we　also　propose　a　two-stage　isolated　optimization　strategy　for　better　convergence.　We　evaluate　our　method　on　a　real-world　stream　monitoring　dataset.　Our　extensive　experiments　demonstrate　that　the　proposed　method　outperforms　several　state-of-the-art　methods　in　both　data　imputation　and　prediction　performance.　©　2022　IEEE.