On the notion that the Reynolds stresses are transported with different time scale depending on the transport direction, the third order velocity correlations are represented by a new turbulent gradient transport model with tonsorial Lagrangian time scale. In order to verify the proposed model, DNS data are first obtained in a turbulent channel flow at Re = 180 and tonsorial Lagrangian time scales are computed. The present model predictions are compared with DNS data and those predicted by the third-order turbulent transport model of Hanjalic and Launder that uses a scalar time scale. The result demonstrates that the Reynolds stresses are indeed transported with different time scale depending on the transport direction.