Carboxyl groups at the periphery of reduced graphene oxide (RGO) sheets are converted to amine groups by reaction with N-hydroxysuccinimide and 1,3-diaminopropane, and a free-radical polymerization initiator is anchored to the RGO sheets. Poly(acrylamide) (PAM) polymer brushes on RGO sheets (RGO/PAM) are synthesized by in situ free-radical polymerization. The heavy metals, Pb(II), and the benzenoid compounds, methylene blue, (MB) were selected and adsorbed by RGO/PAM composites, and the adsorption capacity of RGO/PAM for Pb(II) and MB was measured. The experimental data of RGO/PAM isotherms for Pb(II) and MB followed the Langmuir isotherm model. The RGO/PAM displays adsorption capacities as high as 1000 and 1530 mg/g for Pb(II) and MB, respectively, indicating RGO/PAM is a good adsorbent for the adsorption of Pb(II) and MB. The adsorption kinetics of Pb(II) and MB onto RGO/PAM can be well fitted to the pseudo-second-order model. The adsorption processes of Pb(II) and MB onto RGO/PAM are spontaneous at 298, 308, and 318 K.