We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, Tc, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T Tc, and zero magnetic field, the density of states is characterized by a small gap Eg ≤ Tc resulting from the collective proximity effect. Transverse magnetic field Hg(T) ∝ Eg is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field Hg2(T).