We present a maximally symmetric Two Higgs Doublet Model (2HDM), where the scalar potential possesses an Sp(4)/Z_2 symmetry in the \Phi-space which is isomorphic to SO(5) in the bilinear field space. The usual custodial symmetries of the 2HDM potential are identified as certain subsets of this maximal symmetry group. We analyze the mass spectrum for the charged (H^+, H^-), CP-even scalar (h, H) and CP-odd pseudoscalar (A) Higgs bosons in this minimal model. Starting from the SO(5)-symmetric limit of the theory with four Goldstone bosons (h, A, H^+, H^-) at some high scale, we find that the renormalization group effects still leave the pseudoscalar Higgs boson massless at the weak scale, which can be identified as a U(1)_PQ axion. Introducing a soft symmetry-breaking mass term, we obtain a viable low-energy Higgs spectrum for a range of model parameter space, which is consistent with the current experimental limits, and may be testable in future Higgs precision measurements.