Automated Dialogue Systems, computers that can converse with a human user, are common these days, from phone conversation agents and iPhone Siri to Facebook chat bots. These systems are often trained using Statistical and Machine Learning methods in order to coherently interact with a user and understand their needs to successfully provide necessary information or services. However, training and evaluating these systems can be expensive and laborious if done by a human, since they would need to have hundreds or even thousands of training conversations with the agent using even state-of-the-art training methods. An ideal solution to this is using a User Simulation, where a statistical model of a user is built and used to perform these trial interactions with the dialogue agent in place of a human user. Our work introduces a data-driven approach to building a User Simulation model using a Convolutional Neural Network (CNN), which is conventionally used for image recognition applications. The CNN takes a history of dialogues encoded as vectors and predicts the next dialogue the user would say in response, in the given scenario. We train this model on an existing dataset to show this outperforms the baseline n-gram model and an LSTM-based Sequence-to-Sequence model in terms of F-Score by a significant margin.