It is useful to analyze any optical system theoretically before proceeding with its design in order to ensure the effectiveness of the design through computer simulations that are important and useful in designs for the ability to predict the performance of solar concentrator under any conditions.  For this design, non-sequential ray tracing mode wasused in the Zimax program with a light source that simulated solar radiation.  The purpose of the design of a compound parabolic concentrator (CPC) is to take advantage of the solar radiation that falls on it without the need for an efficiently tracked system within certain limits of the angle of solar radiation fall known as the acceptance angle.  That is, obtaining the largest possible number of rays received inside the CPC through reflections in the inner walls of it, which give a large amount of thermal energy to the surface of the recipient, which in turn gets this energy to be used to create electrical energy. The efficiency of receiving reflected solar radiation in this type of concentrator is great compared to other solar concentrators. Simulated design of solar reflector concentrator has been presented. The concentrator is a type of compound parabolic concentrator (CPC) involved of internal reflector surface (Hollow and within Poly methyl methacrylate (PMMA) polymer material) without tracking system. CPC has the property to overcome problems result from variation of incidence angle of the sun during daytime. Because the tracking system expensive and has technical problems. The efficiency of CPC has been obtained by using Zemax optical design program, for different designs has concentration ratio(c=1,2,3,4,5). That is, the ratio of the output aperture to the input aperture. Taking into account the angle of acceptance that plays a major role in the form of design and its efficiency the results are shown when designing the model with radial aperture of (50mm) and length of (500mm).The design of concentrations ratio is depends on the acceptance angle. c=5 at normal incident angle (ÆŸ=0). And it is almost similar if the material is used PMMA within CPC, and degradation of efficiency with increasing the incidence angle.