A modified trial solution of Wu’s function depending on three parameters and satisfying the boundary conditions, is used as a solution to the Thomas-Fermi equation using variational methods. The found solution is used to calculate the total ionization energy of atoms, taking into account a correction to this equation. Our results show that the proposed generalization is much better than Wu’s one, being in agreement with other solutions found in literature. Our solution, reproduces conveniently the corresponding numerical solution.