Abstract The 2D Hubbard model is the simplest model that possibly explains the occurrence of high- T c superconductivity (SC) in cuprates. To demonstrate this possibility with a condition of moderate on-site Coulomb energy U, we have computed the SC condensation energy E cond by means of the variational Monte Carlo method employing a slightly modified Gutzwiller trial wave function which also takes account of the Bi2212-type band, i.e., t′ ∼ −0.34 and t″ ∼ 0.23 ( t, t′ and t″ are defined in the main text; energy unit is t). The competing SDW E cond strongly depended on the employed lattice size L × L but approached the bulk-limit value when L ⩾ 16. With proper assumption on the value of t″, the t′ region where the SDW E cond are larger than the SC E cond shrank to −0.16 ⩽ t′ ⩽ −0.08. In −0.40 < t′ < −0.16 the SC E cond was found predominant. Concerning the lattice-size dependence the SC E cond in the neighborhood of the Bi2212-type set was found to tend to increase with increasing L when L ⩾ 16, taking about 1/3 or 1 times the experimental SC E cond of YBCO. This was computed using periodic boundary conditions (bc’s) for the two directions. The average of two results for periodic and antiperiodic bc’s imposed to both x- and y-directions for t′ = −0.31 and t″ = 0.21 proved to make the L-dependence so mild that the extrapolation to the finite bulk limit looks plausible. Together with the previous positive result with t′ ∼ −0.05 and t″ = 0, this result clearly supports the applicability of the 2D Hubbard model to the SC in the whole group of cuprates. Incidentally, more elaborate Gutzwiller–Jastrow-type trial functions were also examined but found to bring in only minor differences.