User Simulators are one of the major tools that enable offline training of task-oriented dialogue systems. For this task the Agenda-Based User Simulator (ABUS) is often used. The ABUS is based on hand-crafted rules and its output is in semantic form. Issues arise from both properties such as limited diversity and the inability to interface a text-level belief tracker. This paper introduces the Neural User Simulator (NUS) whose behaviour is learned from a corpus and which generates natural language, hence needing a less labelled dataset than simulators generating a semantic output. In comparison to much of the past work on this topic, which evaluates user simulators on corpus-based metrics, we use the NUS to train the policy of a reinforcement learning based Spoken Dialogue System. The NUS is compared to the ABUS by evaluating the policies that were trained using the simulators. Cross-model evaluation is performed i.e. training on one simulator and testing on the other. Furthermore, the trained policies are tested on real users. In both evaluation tasks the NUS outperformed the ABUS.