We have studied the adsorption of flexible polyelectrolytes on a flat and oppositely charged surface using a field-theoretic approach. Our Hamiltonian includes the entropy of all species (i.e., polyions, solvent and small ions), short-range interactions (e.g., solvent quality) and electrostatic interactions in the system. To incorporate the fluctuation and correlation effects ignored in the mean-field (i.e., self-consistent field) theory, we expand the Hamiltonian to the third-order with a coupling parameter; this results in stronger charge inversion than predicted by the mean-field theory. We further compare our results with relevant theoretical and simulation studies.