To obtain nanofiltration membranes with high-performance in desalination and water purification, membranes of graphene oxide (GO), reduced graphene oxide (rGO) and GO/polyacrylamide (PAM) are prepared by a vacuum filtration method. This method is conducted in aqueous solution without any organic solvents. The graphene-based membranes (GBMs) are characterized by UV-visible spectroscopy, Fourier-transform infrared spectroscopy, transmission electron microscopy, atomic force microscopy, scanning electron microscopy, thermogravimetric analysis and X-ray photoelectron spectroscopy. The hydrophilicity of GBMs is also evaluated by contact angle measurement. The interlayer spacing of GO membrane (0.85nm), GO/PAM membrane (0.68nm) and rGO membrane (0.36nm) are measured by X-ray diffraction. The performance of the GBMs is evaluated on a dead-end filtration device. The water flux and retention of rhodamine B of the membranes are 399.04Lm(-2)h(-1)bar(-1) and 85.03% (GO), 188.89Lm(-2)h(-1)bar(-1) and 95.43% (GO/PAM), 85.85Lm(-2)h(-1)bar(-1) and 97.06% (rGO), respectively. The GO/PAM membrane has the best comprehensive separation performance because of its proper interlayer spacing. GO/PAM membranes provide potential advantages in the design of high-performance membranes for molecular separation and water purification.