Deep learning models have demonstrated high-quality performance in areas such as image classification and speech processing. However, creating a deep learning model using electronic health record (EHR) data, requires addressing particular privacy challenges that are unique to researchers in this domain. This matter focuses attention on generating realistic synthetic data while ensuring privacy. In this paper, we propose a novel framework called correlation-capturing Generative Adversarial Network (CorGAN), to generate synthetic healthcare records. In CorGAN we utilize Convolutional Neural Networks to capture the correlations between adjacent medical features in the data representation space by combining Convolutional Generative Adversarial Networks and Convolutional Autoencoders. To demonstrate the model fidelity, we show that CorGAN generates synthetic data with performance similar to that of real data in various Machine Learning settings such as classification and prediction. We also give a privacy assessment and report on statistical analysis regarding realistic characteristics of the synthetic data. The software of this work is open-source and is available at: https://github.com/astorfi/cor-gan.