A computational investigation has been carried out in the field of charged-particle optics. The work is concerned with the design of einzel (uni potential) lens by using non-classical variation method under different magnification conditions. The potential field distribution of the einzel lens has been represented by an analytical function. The paraxial ray equation has been solved for finding the short beam trajectory of the charged particles traversing the lens. The axial potential distributions and its first and second derivatives, the optical properties such as the focal length and spherical and chromatic aberrations are determined by using non-classical variation method. The electrode shape of the einzel lens has been determined in the two dimensions. The aberrations of the electrostatic lens from our results depend on the beam trajectory of the charged particles, where the aberration is small when the beam trajectory is shorter.