  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 $b\bar{b}$ 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.
