The discovery of nearly room-temperature superconductivity in superhydrides has motivated further materials research for conventional superconductors. To realize the moderately high critical temperature (Tc) in materials containing light elements, we explored new superconducting phases in a scandium borocarbide system. Here, we report the observation of superconductivity in a new ternary Sc-B-C compound. The crystal structure, which was determined through a Rietveld analysis, belongs to tetragonal space group P4/ncc. By complementarily using the density functional theory calculations, a chemical formula of the compound was found to be expressed as Sc20C8-xBxC20 (x = 1 or 2). Interestingly, a small amount of B is essential to stabilize the present structure. Our experiments revealed the typical type-II superconductivity at Tc = 7.7 K. Additionally, we calculated the density of states within a first-principles approach and found that the contribution of the Sc-3d orbital was mainly responsible for the superconductivity.