We report graphene composite membranes with nominal areas more than 25 mm(2) fabricated by transfer of a single layer of CVD graphene onto a porous polycarbonate substrate. A combination of pressure-driven and diffusive transport measurements provides evidence of size-selective transport of molecules through the membrane, which is attributed to the low-frequency occurrence of intrinsic 1-15 nm diameter pores in the CVD graphene. Our results present the first step toward the realization of practical membranes that use graphene as the selective material.