  We update cosmological bound on axion model. The contribution from the
anharmonic effect and the newly introduced initial overshoot correction are
considered. We present an explicit formula for the axion relic density in terms
of the QCD scale Lambda_{QCD}, the current quark masses m_q's and the
Peccei-Quinn scale F_a, including firstly introduced 1.85 factor which is from
the initial overshoot.
