  We calculate the tunneling conductance of a graphene normal
metal-insulator-superconductor (NIS) junction with a barrier of thickness $d$
and with an arbitrary voltage $V_0$ applied across the barrier region. We
demonstrate that the tunneling conductance of such a NIS junction is an
oscillatory function of both $d$ and $V_0$. We also show that the periodicity
and amplitude of such oscillations deviate from their universal values in the
thin barrier limit as obtained in earlier work [Phys. Rev. Lett. {\bf 97},
217001 (2006)] and become a function of the applied voltage $V_0$. Our results
reproduces the earlier results on tunneling conductance of such junctions in
the thin [Phys. Rev. Lett. {\bf 97}, 217001 (2006)] and zero [Phys. Rev. Lett.
{\bf 97}, 067007 (2006)] barrier limits as special limiting cases. We discuss
experimental relevance of our results.
