Graphene oxide (GO) composite nanofiltration membranes (GO-EDA/Al2O3 membrane) cross-linked by ethylenediamine (EDA) were fabricated on dopamine (PDA) modified alumina ceramic membranes. The covalent bonds enhance the interlayer and interface stability of the as-prepared membranes. A method that can simply adjust the layer spacing of GO composite membranes was proposed. The number of hydroxyl groups inside the GO composite membranes can be changed through varying the drying temperature, thus affecting the pure water permeation and salt rejection of the GO composite membranes. The results show that the thickness of the GO composite membranes fabricated at the drying temperature of 40 ℃ is 50-120 nm. The pure water permeance and the rejection towards Na2SO4 solution are 34 L/(m2·h·MPa) and 87.8%, respectively. The GO composite membranes still remain an excellent stability and a high rejection rate after being immersed in pure water for 680 h.