The characteristics of the planar ladder-type multi-gap resonant cavity are investigated, including the mode distribution, characteristic impedance (R/Q), coupling coefficient and the operating stability. The high-frequency interaction system for a W-band high-power extended interaction klystron was designed. The nonlinear performances such as the saturated power, gain, efficiency, as well as bandwidth are predicted by using the three-dimension Particle-in-Cell technology. The modulation and bunching of the beam and the physics of the interaction between the beam and the multi-gap resonant cavity were explored. PIC simulation results show that the output power is up to 1.8kW at the frequency of 94.52GHz with the voltage of 16 kV and beam current of 0.6 A. This power corresponds to a gain of 47.7dB and an efficiency of 19.4% respectively. The sweep-frequency simulations with the same drive power show that the 3-dB bandwidth of 210MHz can be achieved.