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Objectives: Interferogram filtering is the key to the subsequent processing steps of interferometric synthetic aperture radar, such as phase unwrapping and geocoding. However, the existing filtering methods can't retain features in dense fringes and accurately estimate phase in low-coherence regions. The convolutional neural networks (CNN) is introduced to learn noise features and solve this problem. Methods: First, we selected a certain number of interferograms as samples, and divided them into training set, test set, and validation set. Second,we preprocessed the training set samples, and cut the preprocessed training set interferograms into small fixed-size block and randomly extract it as a model training sample, used the above steps to train the autoencoder filter model, after a certain number of iterations, the model was fitted. Results: Experiments were carried out on spaceborne imaging radar-C-band synthetic aperture radar data and Sentinel-1A data. Our proposed method was compared with Goldstein filter, mean filter, Lee filter, Frost filter, and improved denoising convolutional neural network (DnCNN). Goldstein filter can remove most of the noise while maintaining fringes edge, has good denoising ability. Mean filter performs well in high-coherence areas, but performs poorly in low-coherence areas, and can't filter noise well. Lee filter maintains it well image resolution, but the denoising effect is weak, and it can be seen from the filtering results that there is still a lot of noise. Frost filtering is weak in low-coherence areas and there is a lot of noise, but the fringe edges are well maintained in high-coherence areas. The improved DnCNN filter can significantly eliminate the noise, but it can't distinguish the fringe edge and the noise well. Our proposed method can suppress the noise very well, and it can maintain the fringe edge well in the low-coherence area and the high-coherence area. Conclusions: This proposed method can greatly improve the phase quality of the interferogram, suppress the noise to a greater extent, and restore more image details and maintain the edge continuity of the interference fringe. [ABSTRACT FROM AUTHOR]