We report on the superconducting (SC) properties of Y$_2$C$_3$ with a relatively high transition temperature $T_{rm c}=15.7$ K investigated by $^{13}$C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The $^{13}$C Knight shift has revealed a significant decrease below $T_{rm c}$, suggesting a spin-singlet superconductivity. From an analysis of the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ in the SC state, Y$_2$C$_3$ is demonstrated to be a multigap superconductor that exhibits a large gap $2Delta/k_{rm B}T_{rm c}=5$ at the main band and a small gap $2Delta/k_{rm B}T_{rm c}=2$ at other bands. These results have revealed that Y$_2$C$_3$ is a unique multigap s-wave superconductor similar to MgB$_2$.
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