This paper addresses the problem of time-constrained leader-follower multi-agent task scheduling and control synthesis. The leader-follower multi-agent system is subject to a set of dynamically activated tasks, each of which is associated with a relative deadline and can be completed at different Quality-of-Satisfaction levels. By taking into account the reward and cost of satisfying these tasks, a novel scheduling problem is formulated and a dynamic scheduling strategy is proposed. Based on the dynamic plan, distributed control laws are designed accordingly for the leader and follower agents. Under the condition that the information of the target regions are available only to the leader agents, it is shown that the proposed control laws guarantee the satisfaction of each task at its desired Quality-of-Satisfaction level. A simulation example is given to verify the theoretical results.