The light propagation within an absorbing medium and the refraction at the interface between absorbing medium are studied. By using the unit vectors denoting the planes of constant field amplitude and constant phase respectively, with the expression for the light propagation, using the corresponding boundary conditions, the refractive angle of the light through the interface of two absorbing medium have been obtained. This work can be applied to the refraction event at the interface of the media, wherein either/both of them is/are absorbing or transparent. Numerical analysis shows that, the refraction angle depend not only on the incident angle, the complex refractive index of medium but also on the angle between the two unit vectors, and the angle of refraction increases first and then decreases during the increasing of incident angle; the angle between the unit vectors has greater effects on refraction angle in absorbing medium/transparent medium than in the two absorbing medium interface.