Moving monitoring query on moving objects is an important type of query in location based services. Existing solutions suffer from high communication cost. In this paper, we propose a distributed solution to this problem. Our approach employs two ways of communications, on-demand access and broadcast channel, to reduce communication cost. Two different indexes are proposed and evaluated using simulations. The performance results indicate that our solution achieves from 30% to 60% savings in communications when compared to MobiEyes.