We study in this paper both the stationary and time-dependent pseudo-Hermitian Hamiltonians consisting respectively of SU(1, 1), SU(2) generators. The pseudo-Hermitian Hamiltonians can be generated from kernel Hermitian-Hamiltonians by a generalized gauge transformation with a non-unitary but Hermitian operator. The metric operator of the biorthogonal sets of eigenstates is simply the square of the transformation operator, which is formulated explicitly. The exact solutions of pseudo-Hermitian Hamiltonians are obtained in terms of the eigenststates of the Hermitian counterparts. We observe a critical point Gc of coupling constant, where all eigenstates of the stationary Hamiltonians are degenerate with a vanishing eigenvalue. This critical point is modified as Gc(ω) in the time-dependent case including the frequency of external field. Returning to the original gauge we obtain analytically the wave functions and associated non-adiabatic Berry phase, which diverges at the critical point for the SU(2) Hamiltonian. Beyond the critical point Berry phase becomes a complex domain.

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