In this paper, let A and B be n × n × p complex tensors and B = A + E. Denote the T-Drazin inverse of A by A D. We give a perturbation bound for B D − A D /A D under condition (W). Considering the solution of singular tensor equation A * x = b, (b ∈ R(A D)) at the same time. The optimal perturbation of T-Drazin inverse of tensors and the solution of a system of tensor equations have been given.