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Penalized iterative algorithm, which outperforms the maximum likelihood reconstruction by utilizing the image's prior, has became a standard reconstruction approach in PET (Positron Emission Tomography). Such an algorithm is usually called PML (Penalized Maximum likelihood) algorithm. However, this kind of method still suffers from noisy propagation and edge blurring. Recently, the MRP-like (Maximum Root Prior) reconstruction which combines with anisotropic diffusion filtering, taking PDEMedian (Partial Differential Equations Median) for example, was proposed for noise removing and it could obtain better results than traditional algorithms. However, due to the shortcoming of P-M diffusion model, step artifacts could still be observed in the reconstructed image. This work aims to improve the quality of PET images using a novel nonlocal fuzzy diffusion model. Compared to the PDEMedian method, the proposed approach can impose an effective edge-preserving and noise-removing diffusion model for PET image reconstruction. Experimental results showed that the proposed method is more effective in improving quality of reconstructed images comparing with other common methods.