Janus materials have distinct surfaces on their opposite faces. Graphene, a two-dimensional giant molecule, provides an excellent candidate to fabricate the thinnest Janus discs and study the asymmetric chemistry of atomic-thick nanomembranes using covalent chemical functionalisation. Here we present the first experimental realisation of nonsymmetrically modified single-layer graphene--Janus graphene--which is fabricated by a two-step surface covalent functionalisation assisted by a poly(methyl methacrylate)-mediated transfer approach. Four types of Janus graphene are produced by co-grafting of halogen and aryl/oxygen-functional groups on each side. Chemical decorations on one side are found to be capable of affecting both chemical reactivity and physical wettability of the opposite side, indicative of communication between the two grafted groups. This novel asymmetric structure provides a platform for theoretical and experimental studies of two-dimensional chemistry and graphene devices with multiple functions.