With the continuous increase of output power ratings, multi-phase (multichannel) interleaved power factor corrector (IPFC) is gradually employed in domestic and commercial inverter air-conditioners. IPFC can solve several main problems, such as power rating increase, power device selection, input current ripple reduction as well as inductor on-board mounting. But for a multi-phase IPFC, the key problem is that it should show rapid dynamic responds and good current sharing capability, so in this paper the aim is to improve the dynamic performance and current sharing capability by means of passivity control theory. Considering the power circuit topology of a four-phase IPFC, an EL (Euler-Lagrange) mathematical model is established when the IPFC operates in continuous conduction mode (CCM). Then the passivity of the four-phase IPFC is proved, and the passivity-based controller using the state variables feedback and damping injection method is designed. The proposed control scheme, which is easy to control and needs no proportion integral controller, has strong robustness on disturbance from singlephase AC input voltage, the load as well as the parameters of the employed devices. Even in wide-range load condition, the mains current has a fast dynamic response and the average output voltage almost keep unchanged. As a result, the main functions of the four-phase IPFC are implemented including nearly unitary power factor and constant DC output voltage. Meanwhile, the four-phase IPFC acquires an excellent current sparing effect after using passivity-based controller. The above analysis has been proved with simulated results by means of MATLAB/SIMULINK and experimental results, showing that the passivity-based IPFC controller has superior performances and feasibility.