Based on material point method (MPM), tied interface grid material point method is proposed here for localized extreme deformation problems. MPM uses material points to discretize material domain, but uses a regular mesh with uniform cells as background grid to integrate momentum equations and to calculate spatial derivatives in each time step. Such type grid used as a finite element mesh results in both time and memory consuming for problems with localized extreme deformation, where, in fact, a local refined grid is preferable. Therefore, in the proposed method, the background grid with several cell sizes for different material sub domains can be used for such problems. The interaction between refined grid and coarse grid is implemented by a tied interface method. Several numerical examples including stress wave propagation and penetration problems are studied, which show that the proposed method is with higher efficiency and lower memory requirement than MPM.