The present study covers numerical analysis of a thermionic scanning electron microscope(SEM) column. The SEM column contains an electron optical system in which electrons are emitted and moved to form a focused beam, and this generates secondary electrons from the specimen surfaces, eventually making an image. The electron optical system mainly consists of a thermionic electron gun as the beam source, the lens system, the electron control unit, and the vacuum unit. For a systematic design of the electron optical system, the beam trajectories are investigated through numerical analyses by tracing the ray path of the electron beams, and the quality of resulting image is evaluated from the analysis results.