Abstract: To solve second order ordinary differential equations (ODEs) derived from Finite Element Method of Lines (FEMOL), the exact element theory in FEM analysis is established, and formulas for exact solutions at any point are derived. Combined with Element Energy Projection (EEP) method, two EEP super-convergent schemes, simplified form and condensed form, are proposed for approximate elements. The simplified form uses linear shape functions as the test function, which is simple and convenient with certain degree of super-convergence. The condensed form uses condensed shape functions of degree m as the test function, which is capable of producing optimal O(h2m) super-convergence for both displacements and displacement derivatives at any point on each element. Numerical experiments show that the proposed EEP super-convergent strategy is a successful extension of the EEP method to second order ODEs in FEMOL with all advantages in single ODE problems being reserved.