As an important vacuum electron device, the gyrotron has the capability to generate high peak and average powers in the millimeter-wave and terahertz frequency ranges, holding broad prospects of application in fields such as spectroscopy, radar, communication, and biomedical science. However, conventional gyrotrons inevitably face intense mode competition issues, and the introduction of quasi-optical cavity is expected to significantly alleviate the severity of mode competition. In this study, based on the theory of electron gyrotron oscillation, the innovative combination of quasi-optical cavity and sheet electron beam is proposed with the aim of achieving higher output power and efficiency. Simulation results indicate that under conditions of 40 kV electron voltage and an 8.4 T background magnetic field, the designed quasi-optical gyrotron can generate 6.1 kW of output power at a frequency of 220 GHz, with an electron efficiency of 6.1% and stable operation over a certain duration. The proposed structure in this study may provide a novel solution for gyrotron design operating in high-frequency and even higher harmonic regimes, thus furthering its applications in fields such as radar and controlled nuclear fusion.