In this study, the adaptive low rank denoising based Magnetic Resonance Imaging (MRI) reconstruction method is proposed. This method uses denoising-based approximate message passing algorithm to reconstruct MR images. The adaptive Weighted Schatten p-Norm Minimization (WSNM) method is used as its noise reduction model to study the reconstruction performance of the MR images. And the image block size and the number of similar blocks of WSNM are set adaptively according to the noise standard deviation estimated during the algorithm iteration process. Compared with the MR image reconstruction algorithms proposed in recent years, the experimental results show that the proposed method can get higher Peak Signal-to-Noise Ratio (PSNR) and lower Relative L₂ Norm Error (RLNE) and have the best reconstruction performance.