This paper proposes a deep learning-based motion deblurring method for radar images using point-spread function (PSF) estimations. Motion blur is a common problem in radar imaging due to the movement of the radar platform or the target. The proposed method uses a convolutional neural network (CNN) to learn the mapping between the blurred and sharp images. In addition, the PSF of the motion blur is estimated using a separate CNN. The estimated point spread function (PSF) is utilized in conjunction with the input image to reconstruct a deblurred image. The reconstruction process is further optimized by incorporating the relationship between the input image, PSF, and the ground truth into the training loss term and optimizing it. The network is trained on a large dataset of simulated blurred and sharp radar images with corresponding PSFs. The developed method is evaluated on blurred radar images, subjected to varying degrees and lengths of blur, and compared with state-of-the art methods. The results show that the proposed method outperforms the existing methods both qualitatively and quantitatively. The proposed method can be used for various radar imaging applications, such as target detection and recognition, surveillance and navigation.