A high current density cylindrical electron optics system is designed for extended interaction oscillator, including the design of electron gun and focusing magnetic field. To obtain good beam properties, a theory of ideal circular beam focusing is used in design. The focusing magnetic field is calculated by balancing the radial forces. CST PARTICLE STUDIO simulation under space-charge-limited emission model shows good beam qualities with a parallel beam flow throughout the gun and interaction sections. The simulation result is in good agreement with design theory, the beam mean current density attains 244 A/cm2, fill factor 767%, beam transmission 100%.