A strong-coupling theory of superconductivity has been developed for the two-dimensional Hubbard model. Coulomb correlations among superconducting quasiparticles have been taken into account by using auxiliary boson fields in the U → ∞ limit. The universal relationship between T c /T c m a x and the concentration of holes, as observed experimentally, has been reproduced for the case of d-wave superconductivity. Such universal behavior cannot be obtained within weak-coupling (BCS) theory.