Continual relation extraction is an important task that focuses on extracting new facts incrementally from unstructured text. Given the sequential arrival order of the relations, this task is prone to two serious challenges, namely catastrophic forgetting and order-sensitivity. We propose a novel curriculum-meta learning method to tackle the above two challenges in continual relation extraction. We combine meta learning and curriculum learning to quickly adapt model parameters to a new task and to reduce interference of previously seen tasks on the current task. We design a novel relation representation learning method through the distribution of domain and range types of relations. Such representations are utilized to quantify the difficulty of tasks for the construction of curricula. Moreover, we also present novel difficulty-based metrics to quantitatively measure the extent of order-sensitivity of a given model, suggesting new ways to evaluate model robustness. Our comprehensive experiments on three benchmark datasets show that our proposed method outperforms the state-of-the-art techniques. The code is available at the anonymous GitHub repository: https://github.com/wutong8023/AAAI_CML.