Inserting the switched-inductor structure into a traditional Boost converter can increase its line-to-output voltage ratio significantly, decrease the current stresses in the switching elements, reduce losses, and improve efficiency at the same time, which makes it find wide applications in prospect. The bifurcation and chaos phenomenon occurring in the hybrid step-up converter with switched-inductor structure is studied for the first time so far as we know. The discrete iterated mapping model under continuous current mode is established, while the effects of circuit parameters on system performance are analyzed by using bifurcation diagrams. Not only period-doubling bifurcation, border collision bifurcation, tangent bifurcation and intermittent chaos are found in this converter, but a special phenomenon can also be observed according to the simulation result. With the decrease of the capacitance C and inductance L2, the circuit experiences roughly a period, double-period and quadruple-period, and during the quadruple period, two of the bifurcation lines will cross, which leads to the system exhibiting a period-3 behavior at that point. Finally, the existence of this special phenomenon is confirmed by the typical time-domain waveforms and phase portraits of the converter. Results obtained indicate that there can be more complicated and diversiform phenomena in the hybrid step-up converter with switched-inductor structure than in the traditional low-dimensional Boost converter as the circuit parameters vary.