This paper describes the design methodology for a novel Fresnel lens. The original Fresnel lens is obtained from a plano-convex lens, whose spherical surface is split into a number of divisions (called facets), collapsed onto the flat base. Thus, all the facets of the original Fresnel lens have the same radius as that of the plano-convex lens. The proposed design aims to achieve better ray concentration and reduced spherical aberration than the original Fresnel lens by constructing spherical facets with unequal radii. The centers and radii of facets are constrained so that the ray refracted from the bottom vertex of each facet on one side of the optical axis and the ray refracted from the outer vertex of the corresponding facet on the other side of the optical axis must intersect at the focal plane. The proposed lens design has resulted in a 275% gain in the concentration ratio and a 72.5% reduction in the spherical aberration compared to the original lens of the same aperture diameter and number of facets. The performance of both novel and original Fresnel lenses when used as solar concentrators with a conical coil receiver is evaluated. The novel Fresnel lens led to increased heat gain and resulted in a compact solar collector design.