Abstract: While the finite element method of lines (FEMOL) is a general and powerful semi-analytical and semi-discretised method for two-dimensional BVP, its solution in the discrete direction and the analytical direction does not behave equally well. Using the analogy between the two-dimensional FEMOL and one-dimensional FEM, the present paper proposed the concept of the generalized one-dimensional problem for the two-dimensional FEMOL and then generalized the newly-developed EEP (Element Energy Projection) method for super-convergence computation in one-dimensional FEM to the two-dimensional FEMOL analysis. By applying the proposed EEP superconvergence computation in the post-processing of FEMOL analysis, both super convergent displacements and stresses at any point can be obtained with remarkable properties which not only balances the accuracy of the two directions but also makes the accuracy highly super-convergent. Detailed formulation and numerical examples for two-dimensional Poisson’s equation are given in the paper to demonstrate the feasibility and effectiveness of the method.