Electron correlation corrections to the excitation energy of the lowest-lying singlet exciton state of polyethylene are evaluated with the aid of the quasiparticle energies obtained from second-order many-body perturbation theory and from the second-order inverse Dyson equation. A simple approximation is proposed to avoid the evaluation of the quasiparticle energies for high- and low-lying energy bands, which is particularly problematic in extended-system calculations. The inclusion of both the electron correlation effects and diffuse basis functions is important for the proper description of the exciton state. The electron correlation corrections calculated by this method appear to be too large, probably due to the neglect of the screening effects of the quasiparticle interactions.