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Robust principal component analysis (RPCA) is a powerful tool for solving background separation problems. However, the popular RPCA model doesn’t make useful of the prior rank information in the background separation application, which usually leads to poor performance. To solve this issue, a new dual-weighted robust principal component analysis (DWRPCA) is proposed based on the prior rank information of the low-rank matrix and the sparsity of the sparse matrix. The singular values are weighted to encourage the target rank constraint of the low-rank matrix, and the sparse matrix is reweighted to enhance its sparsity. Experimental results show that the proposed dual-weighted RPCA model leads to high accuracy of background separation, and high robustness for a variety of complex scenes, in comparison with the existing methods.