A scanning electron microscope (SEM) is well known as a measurement and analysis equipment in nano technology, being widely used as a crucial one in measuring objects or analyzing chemical components. It is equipped with an electron optical system that consists of an electron beam source, electromagnetic lenses, and a detector. The present work concerns numerical analysis for the electron optical system so as to facilitate design of each component. Through the numerical analysis, we investigate trajectories of electron beams emitted from a nano-scale field emission tip, and compare the result with that of experimental observations. Effects of various components such as electromagnetic lenses and an aperture are also discussed.