The design of metal-bearing carbon-based materials with unique structures and intriguing properties is highly desirable in the fields of physics, chemistry, and materials science. Here, within swarm-intelligence structure search and first-principles computations, we uncovered several hitherto unknown sodium carbides (i.e., Na4C, Na3C2, NaC, Na2C3, and NaC2) under high pressure. Intriguingly, the C atom arrangement reveals multiple structure evolution behavior with increased carbon content, from isolated anions in Na4C, tetramers in Na3C2, extended chains in NaC, pentagonal rings in Na2C3, to eventually hexagonal rings in NaC2. Among predicted phases, the superconducting critical temperature Tc of NaC2 could approach ∼42 K at 80 GPa, which is slightly higher than the Tc of 39 K in the highest phonon-mediated superconductivity of MgB2 at ambient pressure. This work offers insights into the reaction of carbides containing alkali metals and paves the way for the future investigation of high superconductivity in metal carbide systems.