In this paper, a novel illumination compensation method for face recognition under illumination variations is proposed. Rather than performing illumination compensation in a global way, the proposed method uses low-frequency discrete cosine transform (DCT) coefficients in the logarithm domain to estimate illumination in local areas. To estimate the illumination of every point more precisely, a mean operator is applied to refine the estimation. Experimental results on the CMU PIE database, the Yale Face database B and the Extended Yale Face database B demonstrate that the method is superior in comparison with other existing methods. Furthermore, a simplified version of the method is also proposed. Both theoretical analysis and experimental results demonstrate the validity and high computational efficiency of the simplified version. Performances of the proposed methods under different values of parameters are also discussed in the paper.