Although the Higgs boson found at the LHC is consistent with the minimal Higgs sector the Standard Model, there might exist additional Higgs bosons and thus various aspects of the extended Higgs sector have been studied extensively. Motivated by the observed anomaly of muon g-2, we will consider a specific type of two Higgs doublet models (called type-X) to explore its favored parameter space and prospects of finding the extra Higgs bosons at the LHC. In addition, we will discuss the properties of Higgs-portal dark matter in this context.