We propose and demonstrate a convolutional neural network (CNN)-based fast back projection (FBP) imaging method, which has noise-resistant capability in strong noise conditions. In this method, the desired high-resolution image is constructed from a low-resolution back projection (BP) image using a pre-trained CNN. Compared to the high-resolution imaging with basic BP algorithm, the proposed CNN-based FBP imaging has significantly reduced complexity, enabling a fast imaging speed. Meanwhile, by training the CNN using noiseless images as the desired output, the CNN-based FBP imaging is noiseresistant, which helps to obtain high-quality images in strong noise scenarios. Performance of this CNNbased FBP imaging method is investigated and compared with basic BP imaging and other methods through extensive numerical simulations. The results show that, using a CNN with optimized structure, the proposed method can greatly improve the imaging speed. Meanwhile, high-quality images with improved peak signal to noise ratios (PSNRs) are obtained in low signal-to-noise-ratio (SNR) conditions. This CNN-based FBP imaging method is expected to find applications where high-quality and fast radar imaging is required. INDEX TERMS Synthetic aperture radar, back projection algorithm, fast back projection imaging, convolutional neural network, high-resolution imaging.