In this paper, a new single sample face recognition approach based on lower-upper (LU) decomposition is proposed. The single sample and its transpose are decomposed to two sets of basis images respectively by LU decomposition algorithm. Two approximation images are reconstructed from the two basis image sets respectively by the experimental estimation method. The fisher linear discriminant analysis (FLDA) is used to evaluate the optimal projection space using the new training set consisting of the single sample and its two approximation images for each person. We make two main contributions: one is that we propose to decompose the single sample and its transpose using the efficient LU decomposition algorithm; the other is that we present an experimental estimation method using the fixed image size to evaluate the number of basis images, which are used to reconstruct the approximation image. The experimental results on the FERET and AR face databases indicate that the proposed method is efficient and outperforms several state-of-the-art approaches which are proposed to address the single sample per person problem.