Communication is a crucial factor for the big multi-agent world to stay organized and productive. Recently, Deep Reinforcement Learning (DRL) has been applied to learn the communication strategy and the control policy for multiple agents. However, the practical limited bandwidth in multi-agent communication has been largely ignored by the existing DRL methods. Specifically, many methods keep sending messages incessantly, which consumes too much bandwidth. As a result, they are inapplicable to multi-agent systems with limited bandwidth. To handle this problem, we propose a gating mechanism to adaptively prune less beneficial messages. We evaluate the gating mechanism on several tasks. Experiments demonstrate that it can prune a lot of messages with little impact on performance. In fact, the performance may be greatly improved by pruning redundant messages. Moreover, the proposed gating mechanism is applicable to several previous methods, equipping them the ability to address bandwidth restricted settings.