In this paper, a solar compound-parabolic concentrator (CPC), with the simultaneous enhancement of the geometric concentrator ratio and the receiving angle for a circular absorber, is presented. Herein, the surface-shape model of the novel CPC and its mathematical solution are constructed theoretically. The concentration performance of the proposed CPC is analyzed and compared with that of a traditional CPC. The results show that the ordinate value of the surface-shape starting point decreases when the diameter of the circular absorber increases at the same contingence angle of the proposed CPC with a circular absorber. The ordinate value of the surface-shape starting point is -29 mm when the diameter of the circular absorber is 47 mm and the contingence angle is 5.56°. Moreover, the geometric concentration ratio of this novel CPC decreases with increasing the aperture width angle. In contrast, the permissible receiving angle and the average optical efficiency increase with increasing the aperture width angle. When the aperture width angle is 60°, the geometric concentration ratio, the permissible receiving angle, and the average optical efficiency are 1.16, 74.39°, and 86.77%, respectively. Meanwhile, the energy-flow distribution on the absorber surface of the novel CPC is more uniform than that of the traditional CPC.