In this paper, an adaptive moving mesh method is proposed and applied for solving Allen-Cahn phase-field model. The mesh redistribution is obtained by solving a Poisson like partial differential equation system. A plenty of grid points are clustered within the region with large solution variations, while less grid points are located in the regions with smooth solutions. The Allen-Cahn model is discretized by a semi-implicit finite difference scheme, which will lead to a large sparse linear algebra system. The algebra multigrid method is used to solve the linear system. Numerical experiments show that the proposed adaptive approach is effective in improving resolution and computational efficiency.