Abstract: The present paper presents, for one-dimensional FEM at the present stage, a natural and rational approach called Element Energy Projection(EEP)method for super-convergent calculation of both displacements and stresses at any point in an element in post-processing stage. The proposed method is simple, effective and efficient. A large number of numerical examples consistently show that the accuracy of both displacements and stresses so calculated is well comparable to that of the nodal displacements, i.e. being of order h^2m for elements of degree m with sufficiently smooth solutions.