The real refractive angle of light beam through the wedge-shaped absorbing medium is studied, and the relationship between the real refractive angle and the real and imaginary parts of the complex refractive index is obtained. The results show that, when the refractive index of the air, the complex refractive index and the vertex angle of the wedge-shaped absorbing medium are given, the real refractive angle can be calculated. When two light beams enter vertically into two samples with the same material but different vertex angles, respectively, the real and imaginary parts of the complex refractive index of the absorbing medium can be obtained by inversion if the real refractive angles of light exiting from the beveled edge are measured. The numerical simulation results show that, when the vertex angle is relatively small, the real refractive angle has the approximate linear relationship with the vertex angle. When the vertex angle is relatively large, the real refractive angle changes gently with the increase of vertex angle. In the case of the same real parts, the magnitude of the real refractive angle decreases as the imaginary part of the complex refractive index increases.