Multi-junction solar cells can be economically viable for terrestrial applications when operated under concentrated illuminations. The optimal design of concentrator optics in high concentration photovoltaics (HCPV) systems is crucial for achieving high energy conversion. At a high geometric concentration, chromatic aberration of the primary lens can restrict the optical efficiency and acceptance angle. In order to correct chromatic aberration, multi-material, multi-element refractive elements, hybrid refractive/diffractive elements, or multi-element refractive and diffractive systems can be designed. In this paper, the effect of introducing a diffractive surface in the optical path is analyzed. An example two-stage refractive and diffractive optical system is shown to have an optical efficiency of up to 0.87, and an acceptance angle of up to ±0.55° with a 1600× geometric concentration ratio, which is a significant improvement compared to a single-stage concentrator system with a single material. This optical design can be mass-produced with conventional fabrication methods, thus providing a low-cost alternative to other approaches, and the design approach can be generalized to many other solar concentrator systems with different cell sizes and geometric concentration ratios.