To reduce the negative impact of illumination on face recognition, we propose a new illumination compensation method based on image invariant calculation. This invariant (the sum of compensating angles, SCA) is calculated by summing two lighting angles in the proper-compensated state. The SCA only depends on single light source and can be computed only once for a lighting system. Based on the Frankfurt horizontal plane of a human skull, we propose a geometric face model of human skull structure. According to our face model, the compensating angle is calculated from the SCA for a face image taken in the same lighting system. With this compensating angle, the illumination compensation for a face image is done by an additive operation. The experimental results validate our method on the Yale B face database. Compared with Choi0s methods, our method makes obvious improvement on images with large lighting angle, and is more robust to light change in both horizontal and vertical directions.