A locally optimal preconditioned Newton-Schur method is proposed for solving symmetric elliptic eigenvalue problems. Firstly, the Steklov-Poincaré operator is used to project the eigenvalue problem on the domain Ω \Omega onto the nonlinear eigenvalue subproblem on Γ \Gamma , which is the union of subdomain boundaries. Then, the direction of correction is obtained via applying a non-overlapping domain decomposition method on Γ \Gamma . Four different strategies are proposed to build the hierarchical subspace U k + 1 U_{k+1} over the boundaries, which are based on the combination of the coarse-subspace with the directions of correction. Finally, the approximation of eigenpair is updated by solving a local optimization problem on the subspace U k + 1 U_{k+1} . The convergence rate of the locally optimal preconditioned Newton-Schur method is proved to be γ = 1 − c 0 T h , H − 1 \gamma =1-c_{0}T_{h,H}^{-1} , where c 0 c_{0} is a constant independent of the fine mesh size h h , the coarse mesh size H H and jumps of the coefficients; whereas T h , H T_{h,H} is the constant depending on stability of the decomposition. Numerical results confirm our theoretical analysis.