  We study the lepto-axiogenesis scenario in the minimal supersymmetric KSVZ
axion model. Only one Peccei-Quinn (PQ) field and vector-like fields are
introduced besides the MSSM with the type-I see-saw mechanism. The PQ field is
stabilized by the radiative correction induced by the Yukawa couplings with the
vector-like fields introduced in the KSVZ model. We develop a way to follow the
dynamics of the PQ field, in particular we found a semi-analytical solution
which describes the rotational motion under the logarithmic potential with
including the thermalization effect via the gluon scattering which preserves
the PQ symmetry. Based on the solution, we studied the baryon asymmetry, the
effective number of neutrino, and the dark matter density composed of the axion
and the neutralino. We found that the baryon asymmetry is successfully
explained when the mass of PQ field is $\mathcal{O}({10^6~\mathrm{GeV}})$
($\mathcal{O}({10^5~\mathrm{GeV}})$) with the power of the PQ breaking term
being $10$ ($8$).
