Graph embedding has attracted much more research interests in dimensionality reduction. In this study, based on collaborative representation and graph embedding, the authors propose a new linear dimensionality reduction method called collaborative representation-based locality preserving projection (CRLPP). In the CRLPP, they assume that the similar samples should have similar reconstructions by collaborative representation and the similar reconstructions should also have the similar low-dimensional representations in the projected subspace. CRLPP first reconstructs each training sample using the collaborative representation of the other remaining training samples, and then designs the graph construction of all training samples, finally establishes the objective function of graph embedding using the collaborative reconstructions and the constructed graph. The proposed CRLPP can well preserve the intrinsic geometrical and discriminant structures of high-dimensional data in low-dimensional subspace. The effectiveness of the proposed is verified on several image datasets. The experimental results show that the proposed method outperforms the state-of-art dimensionality reduction.