Based on the generalized Dikin-type direction proposed by Jansenet al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P*(k)-matrix linear complementarity problem (LCP). Form using high-order correctors technique and rank-one updating, the iteration complexity and the total computational tu out asymptotically O((k + 1)n L) and O((k + 1)n3L) respectively.