A computational investigation has been carried out in the field of non-relativistic charged-particle optics using the charge density method as a boundary value problem with the aid of personal computer under the absence of space-charge effects. This work has been concentrated on designing a two-electrode electrostatic immersion lens whose electrodes are cylindrical in shape separated by an air gap. The variable parameters of the two electrodes are the voltage ratio applied on them, the air gap separating them, and their radii. The immersion lens has been investigated under finite and zero magnification conditions. The axial potential distribution of an electrostatic immersion lens has been computed by taking into consideration the distribution of the charge density due to the voltages applied on the two cylindrical electrodes. Potentials have been determined anywhere in space by using Coulomb's law. The paraxial ray equation has been solved with the aid of the computed axial potential distribution in order to determine the trajectory of the charged-particles beam along the lens field using Runge- Kutta method. The axial potential and its first and second derivatives have been used for computing the optical properties of the lens under consideration. The lens focal length and its spherical and chromatic aberrations have taken into account due to their importance from the optical point of view. The computed aberrations have been normalized in terms of the focal length under zero magnification operational conditions and in terms of the magnification under finite magnification conditions. The computational results showed that it is possible to design and hence construct various types of electrostatic lenses with the aid of the charge density method.