An aqueous dispersion of graphene nanosheets (GNs) has been successfully prepared via chemical reduction of graphene oxide (GO) by hydrazine hydrate in the presence of poly(2-ethyldimethylammonioethyl methacrylate ethyl sulfate)-co-(1-vinylpyrrolidone) (PQ11), a cationic polyelectrolyte, for the first time. The noncovalent functionalization of GN by PQ11 leads to a GN dispersion that can be very stable for several months without the observation of any floating or precipitated particles. Several analytical techniques including UV−vis spectroscopy, Raman spectroscopy, X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) have been used to characterize the resulting GNs. Taking advantages of the fact that PQ11 is a positively charged polymer exhibiting reducing ability, we further demonstrated the subsequent decoration of GN with Ag nanoparticles (AgNPs) by two routes: (1) direct adsorption of preformed, negatively charged AgNPs; (2) in-situ chemical reduction of silver salts. It was found that such Ag/GN nanocomposites exhibit good catalytic activity toward the reduction of hydrogen peroxide (H2O2), leading to an enzymeless sensor with a fast amperometric response time of less than 2 s. The linear detection range is estimated to be from 100 μM to 40 mM (r = 0.996), and the detection limit is estimated to be 28 μM at a signal-to-noise ratio of 3.