We examine the type-II two-Higgs-doublet model with a light scalar dark matter (S) after imposing the constraints from the Higgs searches at the LHC and dark matter experiments. We first assume that both CP-even Higgses (h and H) are portals between the dark matter and standard model (SM) sectors, and the CP-odd Higgs (A) and H are heavier than 130 GeV. We find that the dark matter with a mass of 10-50 GeV is disfavored by the joint constraints of the 125 GeV Higgs signal data, the relic density, XENON1T (2018), and Fermi-LAT. Next, we consider a special scenario in which the heavy CP-even Higgs is taken as the 125 GeV Higgs. The light CP-even Higgs is the only portal between the dark matter and SM sectors, and the dark matter mass is slightly below the Higgs resonance. We find that the signal data of the 125 GeV Higgs restrict tan β to be in the range of 1-1.5 for m h < 62 GeV. The gg → A → hZ and bb → h → τ þ τ − channels at the LHC can impose lower limits and upper limits on tan β, respectively. For appropriate values of tan β, λ h , and m h , the dark matter with a mass of 10-50 GeV is allowed by the constraints of the Higgs searches at the LHC and dark matter experiments. For example, tan β is restricted to be in the range of 1.0-1.5 for 10 GeV < m s < 28 GeV, and m h 2m S > 1.12 is excluded for 30 GeV < m S < 50 GeV.