Graphene oxide (GO)-based membranes with tunable microstructure and controlled nanochannels have attracted an increasing interest for various applications in wastewater treatment, desalination, gas separation, organic nanofiltration, etc. However, they showed limited use in water desalination due to their lower stability and separation efficiency. In this work, a class of two-dimensional (2D) GO lamellar membranes have been prepared with controlled pores for efficient and fast separation of ions and dye molecules. The GO membranes are fucntionalized with a star-like 6-armed poly(ethylene oxide) using the simple amidation route under mild conditions. The as-prepared covalently cross-linked networks are chemically steady in aqueous medium and show remarkable selectivity (∼100%) for several probe molecules and 10–100 higher permeance than those of the reported GO-based membranes. Further, such membranes are also used for salt separation and show more than 80% rejection for Pb2+ and Ni2+ salts. Moreover, a 1360 nm-thick membrane shows >99% rejection for NaCl with a good water permeance of up to 120 L m–2 h–1 bar–1. Additionally, these membranes are stable for more than 20 days under different conditions.