Linear　discriminant　analysis　(LDA)　has　been　a　widely　used　supervised　feature　extraction　and　dimension　reduction　method　in　pattern　recognition　and　data　analysis.　However,　facing　high-order　tensor　data,　the　traditional　LDA-based　methods　take　two　strategies.　One　is　vectorizing　original　data　as　the　first　step.　The　process　of　vectorization　will　destroy　the　structure　of　high-order　data　and　result　in　high　dimensionality　issue.　Another　is　tensor　LDA-based　algorithms　that　extract　features　from　each　mode　of　high　order　data　and　the　obtained　representations　are　also　high-order　tensor.　This　paper　proposes　a　new　probabilistic　LDA　(PLDA)　model　for　tensorial　data,　namely,　tensor　PLDA.　In　this　model,　each　tensorial　data　are　decomposed　into　three　parts:　the　shared　subspace　component,　the　individual　subspace　component,　and　the　noise　part.　Furthermore,　the　first　two　parts　are　modeled　by　a　linear　combination　of　latent　tensor　bases,　and　the　noise　component　is　assumed　to　follow　a　multivariate　Gaussian　distribution.　Model　learning　is　conducted　through　a　Bayesian　inference　process.　To　further　reduce　the　total　number　of　model　parameters,　the　tensor　bases　are　assumed　to　have　tensor　CandeComp/PARAFAC　(CP)　decomposition.　Two　types　of　experiments,　data　reconstruction　and　classification,　are　conducted　to　evaluate　the　performance　of　the　proposed　model　with　the　convincing　result,　which　is　superior　or　comparable　against　the　existing　LDA-based　methods.