We discuss the cosmological constraints on QCD axion, while focusing on high scale inflation scenario motivated by the recent detection of the CMB B-mode by BICEP2. It is noted that the most plausible scenario compatible with high scale inflation is that the axion scale is around 10^10 GeV in the present universe, while it was around 10^16 GeV during the inflationary epoch. This suggests that axion scale f_a is determined in connection with SUSY breaking scale m_susy, which would yield a specific relation between the two mass scales, e.g. f_a ~ m_susy or f_a ~ (m_susy M_Pl)^1/2.  We point out that such scenario can be naturally realized in the framework of string theory if the PQ symmetry originates from an anomalous U(1) gauge symmetry which is ubiquitous in string models.