This report is mainly concerned with pinning synchronization of multiagent systems connected via impulsive coupling interactions, referred to as multilayer networks. The goal is to drive the followers to asymptotically synchronize with the leader by given impulsive pinning controllers. First, based on Lyapunov stability theory of impulsive differential equation, a general synchronization criteria is derived. Second, the relations among the least number of pinned nodes needed for reaching complete synchronization (CS), the impulsive strength, and the impulse interval for achieving CS are explored and illustrated . In particular, when the impulsive strength is a constant and the impulse intervals are equivalent, it is found that the least number of pinned nodes needed for achieving CS decreases with decreasing impulse interval, while firstly decreases and then increases with increasing impulsive strength and pinning gain. Finally, numerical simulation are given to verify the theoretical results.