We fabricated MoS2 transistor adopting electric double layer (EDL) as gate dielectric. So far, EDL has realized p-type conducting MoS2 in addition to well-known n-type conduction showing ambipolar operation. In our study, field-effect superconducting transition of MoS2 was realized with maximum T
C around 10 K. This T
C is the highest not only within MoS2 compounds but also among whole TMDs. The highest T
C discovered in this study lies in the carrier density region much smaller than chemically investigated region. Such compounds with small doping level have never been successfully synthesized by chemical method. Furthermore, by combining HfO2 (typical high-k material for FETs) gating with EDL gating, continuous control of carrier density, and thus quantum phase, was demonstrated. As a result, we successfully obtained the phase diagram of MoS2. Interestingly, the T
C exhibits strong carrier density dependence, showing dome-shaped superconducting phase. Superconducting dome in other materials than cuprates has been reported only a few times in doped 2D semiconductors. Since FET charge accumulation is basically two dimensional, our result implies the existence of common mechanism for superconducting dome in 2D band insulators.