Code flaws or vulnerabilities are prevalent in software systems and can potentially cause a variety of problems including deadlock, hacking, information loss and system failure. A variety of approaches have been developed to try and detect the most likely locations of such code vulnerabilities in large code bases. Most of them rely on manually designing code features (e.g. complexity metrics or frequencies of code tokens) that represent the characteristics of the potentially problematic code to locate. However, all suffer from challenges in sufficiently capturing both semantic and syntactic representation of source code, an important capability for building accurate prediction models. In this paper, we describe a new approach, built upon the powerful deep learning Long Short Term Memory model, to automatically learn both semantic and syntactic features of code. Our evaluation on 18 Android applications and the Firefox application demonstrates that the prediction power obtained from our learned features is better than what is achieved by state of the art vulnerability prediction models, for both within-project prediction and cross-project prediction.