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In this paper,the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method.Some dynamical properties of the current-mode controlled fractional-order BuckBoost converter are analysed.The simulation is accomplished by using SIMULINK.Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary.At the same time,the simulation results show that the converter goes through different routes to chaos.