A sub-domain scheme combined with a reduced system is proposed for non-matched interface problems. A two-level condensation scheme (TLCS) is employed for the selection of primary degrees of freedom of each sub-domain. The degrees of freedom of each domain are divided into primary, secondary and interface degrees of freedom. After the reduced system is constructed in sub-domain-level, the penalty frame method, which utilizes a conventional FEM solver, is employed for assembling non-matched subdomains. The present method can construct the reduced system of each domain without coupling with adjacent subdomains. Thus it is remarkably efficient in computation time and does not require a full memory of global system. Numerical examples demonstrate that the proposed method saves computational cost effectively and provides a reduced system which predicts the accurate eigenvalues of global system.