Aiming at improving the output voltage gain and reducing the voltage stress of the switch, the switched-inductor structure was embedded into the interleaved parallel Boost converter instead of the traditional inductor. The discrete mathematical model of peak current controlled interleaved parallel Boost converter with switched-inductor was obtained by using stroboscopic mapping method, and its instability mechanism were studied by means of bifurcation diagrams, phase trajectories and Jacobian matrix eigenvalues. Combining the advantages of parametric resonance perturbation and charge control, a compensation scheme was designed to control the chaos of the unstable system. The results show that the embedding of the switched-inductor can effectively broaden the stability range of the interleaved parallel Boost converter, and through the compensation scheme, the chaotic system returns to the period-1 steady state, which improves the performance and stability of the converter.