Nanostructured graphene oxide (GO) membranes offer outstanding mass transport performances such as ultrahigh water flux and precise molecular sieving and thus have a great potential as a novel filtration platform for energy efficient molecular or ionic separation. However, the structural stability of the GO membranes in aqueous environments remains a challenging problem, which limits its practical application perspective. We, here, report a novel GO composite membrane composed of GO and asymmetrically functionalized Janus GO (JGO) sheets. Single-side functionalized JGO was made by amidation of dodecylamine. Incorporation of JGO in GO film exhibited extraordinary stability in water at broad pH values even under agitation. Moreover, JGO-doped GO composite membrane showed robust integrity in acid or base solutions over months. It exhibits high molecular retention above 95% for uncharged and charged dye molecules, rhodamine B, and brilliant blue G while maintaining water permeability comparable with previously reported GO-based membranes under osmotic pressure. This work significantly expands possibilities for new way to enhance the structural stability in graphene-based or 2D-material membrane and surface-selective functionalization in membrane fabrication for many applications.