The nonlinear dynamics phenomena of a Single-Machine-Infinite Bus power system with periodical load disturbance were studied in this paper: the method of multiple scales was used to develop an approximate primary resonance solution; the stability of the periodic motion was analyzed. According to the bifurcation equation, different bifurcation models of primary resonance with different systematical parameters were presented directly by using C-L method, which shown that the occurrence of this phenomena are closely related to the operational parameters and structural parameters of the power system. The numerical simulation results show that with the amplitude of the excitation changing, this system possess rich dynamic behaviors characterized by period-doubling bifurcations, which are precursors to chaos and loss of synchronism. The results can provide theoretical guidance for the synchronous operation, oscillation and out-of-step of a synchronous generator.