In this talk, we will introduce an inverse iterative method for computing the Perron pair of an irreducible nonnegative third order tensor. The method involves the selection of a parameter in the k-th iteration. For every positive starting vector, the method converges quadratically and is positivity preserving in the sense that the vectors approx-imating the Perron vector are strictly positive in each iteration. It is also shown that near convergence. The computational work of the proposed method is much less than (if we also take the parameter to be 1 directly) that of the NgQiZhou algorithm, which is linearly convergent for essentially positive tensors.