In this talk, we will introduce a type of multigrid method to solve linear and nonlinear eigenvalue problems. The method is designed on the multilevel correction scheme for eigenvalue problems and multigrid method for the linear systems. Based on the coarse space from the multigrid method, a new subspace is constructed for solving the eigenvalue problems with a higher convergence rate than the classical subspace projection method. We will introduce the idea and the applications of the multigrid method for eigenvalue problems.