Photon-counting　spectral　computed　tomography　(PCCT)　reconstructs　multiple　energy-channel　images　to　describe　the　same　object,　where　there　exists　a　strong　correlation　among　all　channels.　In　addition,　reconstruction　of　each　energy-channel　image　suffers　photon　count　starving　problem.　To　make　full　use　of　the　correlation　among　different　channels　to　suppress　the　data　noise　and　enhance　the　tissue　texture　in　reconstructing　each　energy-channel　image,　this　paper　proposed　a　tensor　convolutional　neural　network　(TCNN)　architecture　to　learn　a　tissue-specific　texture　prior　for　PCCT　reconstruction.　Specifically,　we　first　model　the　spatial　texture　prior　information　in　each　individual　channel　using　a　convolution　neural　network,　and　then　extract　the　correlation　information　among　different　energy　channels　by　merging　the　multi-channel　networks.　Finally,　we　integrate　the　TCNN　as　a　prior　into　Bayesian　reconstruction　framework.　To　evaluate　the　tissue　texture　preserving　performance　of　the　proposed　method　for　each　channel,　a　vivid　clinical　phantom　which　can　simulate　the　real　tissue　textures　was　employed.　The　improvement　associated　with　TCNN　is　remarkable　relative　to　simultaneous　algebraic　reconstruction　technique　(SART)　and　tensor　dictionary　learning　(TDL)　based　reconstruction.　The　proposed　method　produced　promising　results　in　terms　of　not　only　preserving　texture　feature　but　also　suppressing　image　noise　in　each　channel.　The　proposed　method　outperforms　the　competing　methods　in　both　visual　inspection　and　quantitative　indexes　of　root　mean　square　error　(RMSE),　peak　signal　to　noise　ratio　(PSNR),　structural　similarity　(SSIM)　and　feature　similarity　(FSIM).　©　2020　SPIE