In order to address small sample size (3S) problem, a new algorithm for implementing linear extension of graph embedding (LGE) based on QR decomposition is proposed, which could be used in face recognition. Different from the traditional approach of dimension reduction by Principle Component Analysis (PCA), the new algorithm applies QR decomposition to implement dimension reduction. Then the LGE is followed and employed for the second feature extraction in the transformed space. Finally, the nearest neighbor classifier is used for classification and recognition. The new algorithm not only can effectively solve 3S problem, but also hold the discriminant information. Experimental results on YALE and PIE face databases show that the algorithm outperforms the traditional method in recognition rates.decomposition