Excellent two-dimensional electrode materials can be used to design high-performance alkali-metal-ion batteries. Here, we propose ReN$_2$ monolayer as a superior two-dimensional material for sodium-ion batteries. Total-energy optimization results in a buckled tetragonal structure for ReN$_2$ monolayer, and our phonon spectrum and elastic moduli prove its dynamical and mechanical stability. Further investigation shows that it is metallic and still keep metallic feature after the adsorption of Na or K atoms, its lattice parameter changes by only 3.2% or 3.8% after absorption of Na or K atoms. Our study shows that its maximum capacity reaches 751 mA h/g for Na-ion batteries or 250 mA h/g for K-ion batteries, and its diffusion barrier is only 0.027 eV for Na atom or 0.127 eV for K atom. The small lattice change, high storage capacity, metallic feature, and extremely low ion diffusion barriers make the ReN$_2$ monolayer become superior electrode materials for Na-ion rechargeable batteries with ultrafast charging/discharging processes.