Based on the principle of edge ray, the theory of differential geometry, and the law of geometrical optical reflection, a general mathematical model of non-imaging solar compound parabolic concentrator (CPC) surface structure is constructed for non-concave surface absorber, and the geometric boundary conditions for solving the model are obtained. The applicability of the general mathematical model is verified for the common circular and upper plate absorbers. The results show that the general principle equation is intuitive and convenient in the process of obtaining the structural parameter equation of CPC surface shape. Based on this method, the CPC structural equation of semi-circular absorber with new structure is obtained, and the correctness of the CPC surface equation of semi-circular absorber is verified by laser experiment.