Based on the residue theorem and degenerate perturbation theory,we derive a new,simple and general formula for Berry phase calculation in a two-level system for which the Hamiltonian is a real symmetric matrix.The special torus topology possessed by the first Brillouin zone (1BZ) of this kind of systems ensures the existence of a nonzero Berry phase.We verify the correctness of our formula on the Su-Schrieffer-Heeger (SSH) model.Then the Berry phase of one-dimensional quantum anomalous Hall insulator (1DQAHI) is calculated analytically by applying our method.Finally,illuminated by this idea,we investigate the Chern number in the two-dimensional case,and find a very simple way to determine the parameter range of the non-trivial Chern number in the phase diagram.