We consider a simple extension of the type-II two-Higgs-doublet model by introducing a real scalar as a candidate for dark matter in the present Universe. The main annihilation mode of the dark matter particle with a mass of around 31-40 GeV is into a b (b) over bar pair, and this annihilation mode suitably explains the observed excess of the gamma-ray flux from the Galactic Center. We identify the parameter region of the model that can fit the gamma-ray excess and satisfy phenomenological constraints, such as the observed dark matter relic density and the null results of direct dark matter search experiments. Most of the parameter region is found to be within the search reach of future direct dark matter detection experiments.