By using geometrical analysis a theoretical study in the field of charge particle optics has been accomplished. The work deals with the design of electrostatic lenses for FEL gun, mainly the design of the electrostatic lenses in the case of finite magnification. paraxial ray equation of the optical axis has been solved to find the axial potential distribution. The conditions of the work are a cylindrical electron gun shape, a pereavance gun not less then 1 μper, and the acceleration constant (ˠ) not less then 5 times the input energy from the gun. With the aid of solution of Laplace's equation the shape of electrodes of electron gun have been obtained. The results of this work are compared with previous works. The comparison shows a good agreement.