Abstract: In this paper we simultaneously explain the excesses of the 750 GeV diphoton, muon g-2 and h -> μtau 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) from a second scalar doublet, which leads to a coupling between P and the SM particles as well as a coupling between A and the vector-like fermions. Such mixing and couplings are strongly constrained by tau -> μgamma, 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 h -> μtau. The 750 GeV resonance decays in exotic modes, such as P -> hA, P -> H Z, P -> H A and P -> W-+/- H--/+ and its width can be dozens of GeV and is sensitive to the mixing angle.