In this paper we simultaneously explain the excesses of the 750 GeV diphoton, muon g-2 and $hto mutau$ in an extension of the two-Higgs-doublet model (2HDM) with additional vector-like fermions and a CP-odd scalar singlet ($P$) which is identified as the 750 GeV resonance. This 750 GeV resonance has a mixing with the CP-odd scalar ($A$) in 2HDM, which leads to a coupling between $P$ and the SM particles as well as a coupling between $A$ and the vector-like fermions. Such a mixing and couplings are strongly constrained by $tautomugamma$, muon g-2 and the 750 GeV diphoton data. We scan over the parameter space and find that such an extension can simultaneously account for the observed excesses of 750 GeV diphoton, muon g-2 and $hto mutau$. The 750 GeV resonance decays in exotic modes, such as $Pto hA$, $Pto HZ$, $Pto HA$ and $Pto W^pm H^mp$, and its width can be dozens of GeV and is sensitive to the mixing angle.
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