It is expected that any global symmetry is explicitly violated by gravity. In QCD axion models, the effective axion potential obtains other terms than QCD contributions due to gravitational violation of the global U(1) Peccei-Quinn (PQ) symmetry, and the minimum of the potential is deviated from the CP-conserving points. In general, the deviation is large enough to invalidate the PQ solution to the strong CP problem. This is called “quality problem“. In this talk, assuming that axionic wormhole is the only source of gravitational violation of U(1) PQ symmetry, we give a novel solution to the quality problem in which a non-minimal gravitational coupling is introduced to suppress the gravitational violation. We discuss our solution for two formulations of the gravity; the metric and the Palatini formulations. We will show that the condition to avoid the quality problem is different between the two formulations.