Evaluation is crucial in the development process of task-oriented dialogue systems. As an evaluation method, user simulation allows us to tackle issues such as scalability and cost-efficiency, making it a viable choice for large-scale automatic evaluation. To help build a human-like user simulator that can measure the quality of a dialogue, we propose the following task: simulating user satisfaction for the evaluation of task-oriented dialogue systems. The purpose of the task is to increase the evaluation power of user simulations and to make the simulation more human-like. To overcome a lack of annotated data, we propose a user satisfaction annotation dataset, USS, that includes 6,800 dialogues sampled from multiple domains, spanning real-world e-commerce dialogues, task-oriented dialogues constructed through Wizard-of-Oz experiments, and movie recommendation dialogues. All user utterances in those dialogues, as well as the dialogues themselves, have been labeled based on a 5-level satisfaction scale. We also share three baseline methods for user satisfaction prediction and action prediction tasks. Experiments conducted on the USS dataset suggest that distributed representations outperform feature-based methods. A model based on hierarchical GRUs achieves the best performance in in-domain user satisfaction prediction, while a BERT-based model has better cross-domain generalization ability.