Transfer learning refers to the transfer of knowledge or information from a relevant source task to a target task. However, most existing works assume both tasks are sampled from a stationary task distribution, thereby leading to the sub-optimal performance for dynamic tasks drawn from a non-stationary task distribution in real scenarios. To bridge this gap, in this paper, we study a more realistic and challenging transfer learning setting with dynamic tasks, i.e., source and target tasks are continuously evolving over time. We theoretically show that the expected error on the dynamic target task can be tightly bounded in terms of source knowledge and consecutive distribution discrepancy across tasks. This result motivates us to propose a generic meta-learning framework L2E for modeling the knowledge transferability on dynamic tasks. It is centered around a task-guided meta-learning problem with a group of meta-pairs of tasks, based on which we are able to learn the prior model initialization for fast adaptation on the newest target task. L2E enjoys the following properties: (1) effective knowledge transferability across dynamic tasks; (2) fast adaptation to the new target task; (3) mitigation of catastrophic forgetting on historical target tasks; and (4) flexibility in incorporating any existing static transfer learning algorithms. Extensive experiments on various image data sets demonstrate the effectiveness of the proposed L2E framework.