  Josephson effect in a planar graphene junction is studied by assuming that
the coupling of a graphene sheet and two superconductors deposited on its top
is described by a tunneling Hamiltonian. This model properly takes account of
the proximity effect characteristic to a planar junction, and allows us to
treat monolayer and bilayer cases in a parallel manner. Applying a
quasiclassical Green's function approach to it we analyze the Josephson
critical current $I_{\rm c}$ in a short-junction limit. As a characteristic
feature of the planar junction we find that $I_{\rm c}$ is a concave function
of temperature at the strong coupling limit while it crosses over to a convex
function with decreasing the coupling strength. We also find different
chemical-potential dependences of $I_{\rm c}$ in the monolayer and bilayer
cases.
