The circuit parameters of Buck-Boost converter with switched-inductor are studied in order to analyze the influence on the performance of the system. The discrete iterated mapping model under discontinuous conduction mode (DCM) is established. The stability problem is studied by bifurcation diagrams and Poincare sections, and the location of the first bifurcating point is confirmed based on the loci of eigenvalue for the system’s Jacobian matrix. Finally, a simulation model is built up by PSIM software to verify the correctness of the theoretical analysis and the rich dynamic process is observed by time-domain diagram and phase track diagram under different parameters. The studied results and analysis methods are helpful for designing and debugging the switched converters like that. The results show when Buck-Boost converter with switched-inductor works in DCM mode, its working states are mainly affected by the border of current I_b2, the current I_b1 border has small impact on the stability of the system. With the change of circuit parameters, the system enters into DCM intermittent chaos state by the border collision bifurcation.