Abstract: Based on the Element Energy Projection (EEP) method, the present paper presents, for one-dimensional Galerkin FEM (Finite Element Method), an improved scheme with an optimal order of super-convergence, i.e. for elements of degree with sufficiently smooth solutions, the proposed scheme is capable of producing super-convergence for both displacements and stresses at any point on any element in post-processing stage. To achieve that, condensed trial shape functions and condensed test shape functions were developed first, and then associated theorems of approximation and equivalence were proved. Based on these theorems, the formulation of the proposed scheme was obtained. Finally a series of typical numerical examples were given, which indicate that this improved scheme can really achieve the optimal order of super-convergence at any point of the solution domain.