We report for the first time the occurrence of superconductivity in the quaternary silicide carbide YRe2SiC with Tc ≈ 5.9 K. The emergence of superconductivity was confirmed by means of magnetic susceptibility, electrical resistivity, and heat capacity measurements. The presence of a well-developed heat capacity feature at Tc confirms that superconductivity is a bulk phenomenon, while a second feature in the heat capacity near 0.5Tc combined with the unusual temperature dependence of the upper critical field Hc2(T) indicate the presence of a multiband superconducting state. Additionally, the linear dependence of the lower critical field Hc1 with temperature resemble the behavior found in compounds with unconventional pairing symmetry. Band structure calculations reveal that YRe2SiC could harbor a non-trivial topological state and that the low-energy states occupy multiple disconnected sheets at the Fermi surface, with different degrees of hybridization, nesting, and screening effects, therefore making unconventional multiband superconductivity plausible.