Many methods for denoising additive white Gaussian images have been developed, such as the use of non-local mean filters (NLF) and deep convolutional neural networks (CNN). However, these denoising methods still have many limitations on compressed images such as JPEG2000 compression. Based on quantization of noisy wavelet coefficients, JPEG2000 may lead to very specific visual artifacts. This compressed image's noise distribution model is highly spatially correlated and very different from the noise distribution model in additive Gaussian white noise images. In this paper, we propose a convolutional neural network structure combined with nonlocal filter. At first a convolutional neural network have been trained by using highly compressed noisy images to obtain a specific noise model estimation and this noise model estimation is used for the residual neural network. Secondly, it based on non-proximity average filtering, where a similar block selection method is modified to find block artifacts in the compressed image and then do denoising. Finally, combining these two methods can get a clear image output. The evaluation results of this method on the grayscale image dataset are better than the latest technology. Contribution- We produced a noise distribution CNN model that can predict the noise of highly compressed images with complex noise distribution, and combine CNN and Nonlocal mean filters to obtain good denoising results.