A copper-based catalyst, which was supported by sulfonate group (−SO3H) grafted active carbon (AC), was prepared and activated simultaneously by liquid phase chemical reduction method. The modified copper catalyst, Cu/AC–SO3H, displayed an enhanced catalytic performance for selective hydrogenation of furfural (FAL) to furfuryl alcohol (FOL) in liquid phase, in which almost 100% FOL yield was obtained at 378 K and 0.4 MPa of hydrogen pressure after 120 min reaction. The effect of −SO3H was evaluated and illustrated by the combination of reaction performance and physicochemical characterizations, such as X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), and X-ray photoelectron spectrometer (XPS) measurements. Through grafting sulfonate group on the support, better dispersion of nanoparticles, higher reduction degree of Cu, and stronger adsorption of FAL can be attained to contribute high hydrogenation performance. In addition, the effects of reaction conditions (such as reaction temperature, H2 pressure, reaction time, solvent, and catalyst to FAL mass ratio) were evaluated intensively. Also, the Cu/AC–SO3H catalyst showed an excellent catalytic performance for transfer hydrogenation of FAL, in which 2-propanol was utilized as the solvent and hydrogen donor concurrently. Cycling test proved the prepared catalyst could be recycled and reused for several times without noticeably reduced catalytic activity of hydrogenation.