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This paper considers the problem of how to reduce communication cost over threshold monitoring in distributed system. An Event-based Threshold Dynamically Assign (ETDA) method is proposed in this paper, which considers the situation in reality that the data distribution in remote monitor nodes changes dynamically. Therefore, we set different threshold value in each remote monitor node based on their object value, and adjustment is taken place when any event (local threshold violation) occurs or a time window is exceeded. The time window is used to guarantee that local threshold assignment will not happen too frequently. We also consider that there are two kinds of messages in the monitoring system, they are pull and push messages. We found that when the communication cost of pulling is the same as the communication cost of pushing, ETDA achieves better performance than the UTA algorithm which set local threshold uniformly and statically. Experimental evaluation shows the efficiency of ETDA on reduce communication over threshold monitoring in distributed system.