Two major challenges in applying deep learning to develop a computer-aided diagnosis of fundus images are the lack of enough labeled data and legal issues with patient privacy. Various efforts are being made to increase the amount of data either by augmenting training images or by synthesizing realistic-looking fundus images. However, augmentation is limited by the amount of available data and it does not address the patient privacy concern. In this paper, we propose a Generative Adversarial Network-based (GAN-based) fundus image synthesis method (Fundus GAN) that generates synthetic training images to solve the above problems. Fundus GAN is an improved way of generating retinal images by following a two-step generation process which involves first training a segmentation network to extract the vessel tree followed by vessel tree to fundus image-to-image translation using unsupervised generative attention networks. Our results show that the proposed Fundus GAN outperforms state of the art methods in different evaluation metrics. Our results also validate that generated retinal images can be used to train retinal image classifiers for eye diseases diagnosis. Clinical Relevance- Our proposed method Fundus GAN helps in solving the shortage of patient privacy-preserving training data in developing algorithms for automating image- based eye disease diagnosis. The proposed two-step GAN- based image synthesis can be used to improve the classification accuracy of retinal image classifiers without compromising the privacy of the patient.