The discovery of nearly room-temperature superconductivity in superhydrides has motivated further materials research for conventional superconductors. To realize the moderately high critical temperature (T-c) 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 T-c = 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.