  We propose a minimal model for the Josephson current through a quantum dot in
a Kondo regime. We start with the model that consists of an Anderson impurity
connected to two superconducting (SC) leads with the gaps
$\Delta_{\alpha}=|\Delta_{\alpha}| e^{i \theta_{\alpha}}$, where $\alpha = L,
R$ for the lead at left and right. We show that, when one of the SC gaps is
much larger than the others $|\Delta_L| \gg |\Delta_R|$, the starting model can
be mapped exactly onto the single-channel model, which consists of the right
lead of $\Delta_R$ and the Anderson impurity with an extra onsite SC gap of
$\Delta_d \equiv \Gamma_L e^{i \theta_L}$. Here $\theta_L$ and $\Gamma_L$ are
defined with respect to the starting model, and $\Gamma_L$ is the level width
due to the coupling with the left lead. Based on this simplified model, we
study the ground-state properties for the asymmetric gap, $|\Delta_L| \gg
|\Delta_R|$, using the numerical renormalization group (NRG) method. The
results show that the phase difference of the SC gaps $\phi \equiv \theta_R
-\theta_L$, which induces the Josephson current, disturbs the screening of the
local moment to destabilize the singlet ground state typical of the Kondo
system. It can also drive the quantum phase transition to a magnetic doublet
ground state, and at the critical point the Josephson current shows a
discontinuous change. The asymmetry of the two SC gaps causes a re-entrant
magnetic phase, in which the in-gap bound state lies close to the Fermi level.
