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Linear subspace learning (LSL) is a popular approach to image recognition and it aims to reveal the essential features of high dimensional data, e.g., facial images, in a lower dimensional space by linear projection. Most LSL methods compute directly the statistics of original training samples to learn the subspace. However, these methods do not effectively exploit the different contributions of different image components to image recognition. We propose a novel LSL approach by sparse coding and feature grouping. A dictionary is learned from the training dataset, and it is used to sparsely decompose the training samples. The decomposed image components are grouped into a more discriminative part (MDP) and a less discriminative part (LDP). An unsupervised criterion and a supervised criterion are then proposed to learn the desired subspace, where the MDP is preserved and the LDP is suppressed simultaneously. The experimental results on benchmark face image databases validated that the proposed methods outperform many state-of-the-art LSL schemes.