A novel video-based gait recognition method aiming at robust and efficient performance is proposed in this work. The proposed method is composed by two main modules: (1) feature extraction via a sequence of subspace projections of the gait energy image (GEI) and (2) recognition via collaborative representation classification (CRC). The first module consists of three GEI subspace projections (GSP) in sequence – projection onto discriminative regions in the spatial domain, projection onto the PCA subspace and projection onto the LDA subspace – and the projection parameters are learned from samples of a wide range of covariate conditions. We attempt to maintain the most discriminating information, enlarge inter-class differences and suppress intra-class variances through these projections. The proposed GSP-CRC method is computationally efficient with good resilience to noise and data corruption. Besides, it mitigates the problem of insufficient templates. It is demonstrated by comprehensive experiments that the proposed GSP-CRC method achieves outstanding performance in recognition rate, computational efficiency and generic applicability in comparison with state-of-the-art gait recognition methods.