Traditional robust principle component analysis (RPCA) has a high computational cost because RPCA needs to calculate the singular value decomposition of large matrices. To address this issue, this paper proposes a matrix-factorization-based RPCA (MFRPCA) model. MFRPCA has high computation efficiency while improving the robustness and flexibility of traditional RPCA using a non-convex low-rank approximation. Experiment results on challenging datasets demonstrate superior performance of MFRPCA compared with several advanced low-rank reconstruction methods.