We revisit dark matter annihilation as an explanation of the positron excess reported recently by the AMS-02 satellite-borne experiment. To this end, we propose a particle dark matter model by considering a Two Higgs Doublet Model (THDM) extended with an additional pseudoscalar singlet and a singlet fermion. The additional (light) pseudoscalar singlet mixes with the pseudoscalar inherent in the THDM, and the singlet fermion, which is the dark matter candidate, annihilate via the pseuodoscalar portal. The dark matter candidate is made leptophilic by choosing the lepton specific THDM and a suitable high value of tan β. After establishing the viability of the singlet fermion to be a dark matter candidate, we calculate the positron execss coming from its annihilation to a pair of heavy Higgs bosons which primarily decay to tau leptons. Considering properly the Sommerfeld effect caused by the light pseudoscalar and an appropriate boost factor, we find that our proposed model can fit well the positron fraction excess data, but poorly the positron spectrum data.