  Let A be a unital AF-algebra (simple or non-simple) and let \alpha be an
automorphism of A. Suppose that \alpha has certain Rokhlin property and A is
\alpha-simple. Suppose also that there is an integer J\geq1 such that
\alpha^{J}_{*0}=id_{K_{0}(A)}, we show that A\rtimes_{\alpha}\mathbb{Z} has
tracial rank zero.
