It is crucial to control the ion transport in membranes for various technological applications such as energy storage and conversion. The emerging functional two-dimensional (2D) nanosheets such as graphene oxide and MXenes show great potential for constructing ordered nanochannels, but the assembled membranes suffer from low ion selectivity and stability. Here a class of robust charge-selective membranes with superhigh cation/anion selectivity, which are assembled with monolayer nanosheets of cationic/anionic clays that inherently have permanent and uniform charges on each layer is reported. The transport number of cations/anions of cationic vermiculite nanosheet membranes (VNMs)/anionic Co-Al layered double hydroxide (CoAl-LDH) nanosheet membranes is over 0.90 in different NaCl concentration gradients, outperforming all the reported ion-selective membranes. Importantly, this excellent ion selectivity can persist at high-concentration salt solutions, under acidic and alkaline conditions, and for a wide range of ions of different sizes and charges. By coupling a pair of cation-selective vermiculite membrane and anion-selective CoAl-LDH membrane, a reverse electrodialysis device which shows an output power density of 0.7W m-2 and energy conversion efficiency of 45.5% is constructed. This work provides a new strategy to rationally design high-performance ion-selective membranes by using 2D nanosheets with inherent surface charges for controllable ion-transport applications.