We study a minimal model for a light scalar dark matter, requiring a light scalar mediator to address the core-cusp problem and interact with the standard model particles. We analyze the model comprehensively by focusing on the Breit-Wigner resonance for dark matter annihilation and self-scattering channels, considering the thermal relic abundance condition that includes the early kinetic decoupling effect, as well as the present and future constraints from collider, direct, and indirect dark matter detections. We found that the scalar dark matter with the mass of 0.3-2 GeV remains uncharted, which will be efficiently tested by the near future MeV gamma-ray observations.