A dome-shaped superconducting region appears in the phase diagrams of many unconventional superconductors. In doped band insulators, however, reaching optimal superconductivity by the fine-tuning of carriers has seldom been seen. We report the observation of a superconducting dome in the temperature-carrier density phase diagram of MoS2, an archetypal band insulator. By quasi-continuous electrostatic carrier doping achieved through a combination of liquid and solid gating, we revealed a large enhancement in the transition temperature T-c occurring at optimal doping in the chemically inaccessible low-carrier density regime. This observation indicates that the superconducting dome may arise even in doped band insulators.