An electron gun for an accelerating voltage of 100 kV to be operated under space charge limited condition is designed and its emittance and brightness are calculated. To obtain low brightness, a pierce-type electron gun with a Wehnelt electrode and a control anode is adopted. Choosing a low value of the ratio between anode and cathode curvatures reduces the electric field strength at the cathode. A maximum emittance of 1.8 mm mrad and a minimum brightness of 350 A/(cm(2) sr) are obtained under the above conditions with a cathode diameter of 1.66 mm. The radius of the Wehnelt aperture and its axial position are optimized. The effects of deviations: of the shapes of the Wehnelt and control electrodes from concentric sphere are studied. It is found that in the space between the anode and the control anode the electrodes must be spherical up to an angle of at least 55 degrees, whereas in the space between the Wehnelt electrode and the control anode the electrodes must be spherical up to an angle of at least 21 degrees.