Graphene oxide (GO) membranes represent a next generation of high-flux, ultra-lightweight and energy-efficient membranes for molecular and ionic separation in aqueous solution. In this work, we fabricate free-standing GO membranes with tunable thickness via facile vacuum filtration process. The effect of electrostatic interaction on the separation performance of GO membrane for organic dyes was demonstrated. It is observed that GO is negatively charged in a wide pH range of 1-12 and its surface charge density significantly varied with pH of aqueous solution. The electronegative GO membrane exhibits much higher rejection rate for electronegative organic dyes than that for electropositive molecules. Furthermore, the rejection rate and the strength of electrostatic interaction are directly related. In addition, the rejection behaviors of GO membranes for inorganic salts with different charge or ionic strength are explored as well. The experimental data are fitted well with the theoretical model based on Donnan equilibrium. Our results indicate that GO membranes could be promising candidate for water treatment and desalination application. And adjusting the surface charge density of GO and filtrated molecules is an effective way to achieve high separation performance (e.g. rejection rate).