The structures and spectroscopic constants of Zn2 and Cd2 were studied using the coupled-cluster theory with spin-orbit coupling based on the two-component relativistic effective core potential and matched basis sets aug-cc-pvnz-pp (n=Q, 5), combining complete basis set extrapolation of the electronic correlation energy and fourth-order polynomial fitting technique. Spin-orbit coupling was included in the post-Hartree-Fock procedure, i.e., in the coupled-cluster iteration, to obtain more reasonable results, although the spin-orbit coupling effect observed in Zn2 and Cd2 is not visible as it is in Hg2. Our theoretical results agree well with the latest experimental values and other groups' theoretical results, and will be helpful in understanding the spectral characteristics of these two dimers.