  We show that in contrast to conventional normal
metal-insulator-superconductor (NIS) junctions, the tunneling conductance of a
NIS junction in graphene is an oscillatory function of the effective barrier
strength of the insulating region, in the limit of a thin barrier. The
amplitude of these oscillations are maximum for aligned Fermi surfaces of the
normal and superconducting regions and vanishes for large Fermi surface
mismatch. The zero-bias tunneling conductance, in sharp contrast to its
counterpart in conventional NIS junctions, becomes maximum for a finite barrier
strength. We also suggest experiments to test these predictions.
