Abstract: For one-dimensional C¹ problems of the Ritz Finite Element Method (FEM), an error estimate of the super-convergent displacement is presented for the simplified form of the Element Energy Projection (EEP) method used for super-convergence computation in post-processing stage of FEM. The mathematical analysis proves that for elements of degree m(>3) with sufficiently smooth problems and solutions, EEP displacement of the simplified form is capable of producing a convergence order of h^m+2 at any point on an element, i.e. being at least one order higher than the displacement from conventional FEM.