Sodium storage capacity, mobility, and volume change during sodiation on the surfaces of interlayer-expanded Ti3C2 MXenes are investigated using ab initio density functional theory. The theoretical results reveal that the interlayer-expanded bare, F-, O-, and OH-functionalized Ti3C2 MXenes exhibit low barriers for sodium diffusion and small changes of lattice constant during sodiation. In addition, enlarged interlayer distance enables the stable multilayer adsorption on the bare and O-functionalized Ti3C2 MXenes and therefore significantly enhances their theoretical capacities. Both bare and O-functionalized Ti3C2 MXenes are predicted to be prospective anode materials for sodium-ion batteries with high theoretical capacities, fast discharge/charge rates, and good cycling performances. The present results provide a new route to improve the battery performances of anode materials based on MXene intercalation hosts.