To benefit the learning of a new task, meta-learning has been proposed to transfer a well-generalized meta-model learned from various meta-training tasks. Existing meta-learning algorithms randomly sample meta-training tasks with a uniform probability, under the assumption that tasks are of equal importance. However, it is likely that tasks are detrimental with noise or imbalanced given a limited number of meta-training tasks. To prevent the meta-model from being corrupted by such detrimental tasks or dominated by tasks in the majority, in this paper, we propose an adaptive task scheduler (ATS) for the meta-training process. In ATS, for the first time, we design a neural scheduler to decide which meta-training tasks to use next by predicting the probability being sampled for each candidate task, and train the scheduler to optimize the generalization capacity of the meta-model to unseen tasks. We identify two meta-model-related factors as the input of the neural scheduler, which characterize the difficulty of a candidate task to the meta-model. Theoretically, we show that a scheduler taking the two factors into account improves the meta-training loss and also the optimization landscape. Under the setting of meta-learning with noise and limited budgets, ATS improves the performance on both miniImageNet and a real-world drug discovery benchmark by up to 13% and 18%, respectively, compared to state-of-the-art task schedulers.