As well as having a significant impact on models beyond the Standard Model, the Higgs boson discovery has opened a new era in both experimental and phenomenological searches. For instance, observed anomalies in Higgs decays into two photons and four leptons and muon anomalous magnetic moment (muon g - 2) may imply more Higgs-like scalars. In this work, we study Two Higgs Doublet Model-TypeIII, in which one Higgs doublet develops a zero vacuum expectation value. we find the mass spectrum include five Higgs bosons each of which is lighter than about 350 GeV. We consider the contributions to muon g - 2 from these light extra Higgs bosons, and we find that the discrepancy between the SM and the experimental measurements can be resolved if m(H), m(A), m(H perpendicular to) less than or similar to 150 GeV.