The dispersion equation of a peniotron using TE_no mode in a rectangular waveguide strusture is derived in this paper. The working conditions of the peniotron are investigated and a clearer explanation of the peniotron is made. Based on this，numerical calcnlations of the dispersion equation of the peniotron using TE₂₀ mode are carried out to get the dispersion curves of the peniotron working at the fundamental and the third harmonic synchronous resonance. The curves show that the peniotron has 1.5% growth rate at the fundamental and 0.8% average growth rate at the third harmonic resonance.Further more，the performance of peniotron at the fundamental and the third harmonic resonance are analysed by nonlinear theory，which gives the electron distribution at efficiency saturation. Through large amount of computation，the optimum result is derived: peniotro has 51%high efficiency and QPw=9949.94MW output power at the fundametal，and 11% efficiency and QPw=1741.8MW output power at the third harmonic resonance.