Spatiotemporal　traffic　data　exhibit　multi-granular　low-rank　structure　due　to　their　periodicity　among　different　timelines.　Traditional　low　rank　data　completion　methods　fail　to　characterize　such　properties　and　produce　unsatisfactory　results　for　data　imputation.　In　this　paper,　a　tensorial　weighted　Schatten-p　norm　minimization　(TWSN)　is　proposed　for　spatiotemporal　traffic　data　imputation.　TWSN　consists　of　an　approximation　term　and　a　low-rank　regularization　term　over　the　recovered　tensor　data,　where　the　latter　is　a　combination　of　the　weighted　Schatten-p　norm　in　the　matrix　form　of　each　mode　of　the　tensor.　For　each　mode,　TWSN　utilizes　a　selection　scheme　of　the　mode-wise　weights　to　capture　different　properties　of　singular　values　of　each　mode　of　the　tensor.　Overall,　TWSN　not　only　plays　a　balancing　role　between　the　rank　function　and　the　nuclear　norm,　but　also　captures　the　anisotropic　correlation　of　singular　values　of　each　mode　of　the　tensor.　TWSN　is　evaluated　on　four　real-world　datasets　with　different　ping　frequencies　(2,　5,　10　min)　and　its　performance　is　compared　with　several　state-of-the-art　methods.　The　experimental　results　show　that　TWSN　outperforms　other　methods　under　various　data　missing　scenarios.