It is shown that the mass difference between η′ and pseudoscalar octet mesons can be calculated in quenched lattice QCD with the aid of a variant wall source technique. The estimated mass difference increases as the quark mass decreases, and its value extrapolated to the zero-quark-mass limit. mη′2-m82=(750±40 MeV)2, is close to the value determined from experiment (850 MeV)2. These results indicate that the long-standing U(1) problem could be solved in lattice QCD, with its essential part being understood within the quenched approximation. We also comment on implications of our results on spurious infrared divergences in quenched QCD.