We study the problem of meta-learning with task-level differential privacy. Meta-learning has received increasing attention recently because of its ability to enable fast generalization to new task with small number of data points. However, the training process of meta learning likely involves exchange of task specific information, which may pose privacy risk especially in some privacy-sensitive applications. Therefore, it is important to provide strong privacy guarantees such that the learning process will not reveal any task sensitive information. To this end, existing works have proposed meta learning algorithms with record-level differential privacy, which is not sufficient in many scenarios since it does not protect the aggregated statistics based on the task dataset as a whole. Moreover, the utility guarantees in the prior work are based on assuming that the loss function satisfies both smoothness and quadratic growth conditions, which do not necessarily hold in practice. To address these issues, we propose meta learning algorithms with task-level differential privacy; that is, our algorithms protect the privacy of the entire dataset for each task. In the case when a single meta model is trained, we give both privacy and utility guarantees assuming only that the loss is convex and Lipschitz. Moreover, we propose a new private clustering-based meta-learning algorithm that enables private meta learning of multiple meta models. This can provide significant accuracy gains over the single meta model paradigm, especially when the tasks distribution cannot be well represented by a single meta model. Finally, we conduct several experiments demonstrating the effectiveness of our proposed algorithms.