Recently, deep learning-based intelligent fault diagnosis methods have been developed rapidly, which rely on massive data to train the diagnosis model. However, it is usually difficult to collect sufficient failure data in practical industrial production, thus limits the application of intelligent diagnosis methods. To address the few-shot fault diagnosis problem, a task-sequencing meta-learning method is proposed in this article. First, the meta-learning model is trained over a series of learning tasks to obtain knowledge about how to diagnosis. Thus, the learned knowledge can help adapt and generalize with a few examples when dealing with new tasks that have never been encountered. Then, considering the difference and connection between different failures and diagnosis tasks, a task-sequencing algorithm is proposed to sort meta training tasks from easy to difficult, which followed the way human acquire knowledge. After evaluating the difficulty of each task, the proposed method learns simple tasks first and generalizes the learned knowledge to complex tasks. Better knowledge adaptability is obtained by gradually increasing the task difficulty. Finally, utilizing gradient-based meta learning, the initialization parameters are trained by a small number of gradient steps. The effectiveness of the proposed method is validated by a practice rolling bearing dataset and a power system dataset. The experiment results illustrate that the proposed method can identify new categories with only several samples. In addition, it also shows advantages in fault diagnosis when the categories are fine-grained according to the working conditions. Therefore, the proposed method is suitable for solving the few-shot problem in practice and complicated fault diagnosis.