The robust principal component analysis （RPCA） model aims to estimate underlying low-rank and sparse structures from the degraded observation data. Both the rank function and the L 0 -norm minimization in the RPCA model are nondeterministic polynominal（NP）-hard problems， which usually are solved by the convex approximation model， so leading to the undesirable over-shrinkage problem. This paper proposes a dual-weighted L p -norm model based RPCA model by combining the weighting method and the L p -norm. We use the weighted S p -norm low-rank term and the weighted L p -norm sparse term to model the low-rank and sparse recovery problems under the RPCA framework， respectively， which provides better approximations to the rank minimization and the L 0 -norm minimization， thus improving the accuracy of the rank estimation and the sparse estimation. To further demonstrate the performance of the proposed model， we apply the dual-weighted L p -norm RPCA model to remove the salt-and-pepper noise by exploiting the image nonlocal self-similarity and combining the low rank of similar image patch matrices and the sparsity of salt-and-pepper noise. Both qualitative and quantitative experiments demonstrate that the proposed model outperforms other state-of-the-art models， and the singular value over-shrinkage analysis experiment also demonstrates that the model can better deal with the over-shrinkage problem of the rank components.