We have attempted to prepare graphene samples by mechanical exfoliation of HOPG (highly oriented pyrolytic graphite) using scotch tape. Random testing of the flakes by AFM has shown in majority single layer graphene. Nevertheless, the presence of ultrathine graphite cannot be excluded in the large assembly of flakes needed for electron spin resonance (ESR) measurements. Graphene flakes sitting on ESR-silent scotch tapes were stacked parallel to form a multilayer sandwich. The ESR measurements performed in the 4–300 K range yielded narrow Lorentzian line. The spin susceptibility was decreasing linearly with decreasing temperature as expected for the conical band dispersion of graphene. Below 70 K the spin susceptibility started to deviate from the linear temperature dependence and a Curie-like behavior was observed. This contribution to the susceptibility is due to the existence of defects or impurities, which are in strong exchange coupling limit with conduction electrons. The temperature dependence of the linewidth suggests Elliott's mechanism for spin relaxation in graphene flakes.