The continuous top-t most influential place (CTtMIP) query is defined formally and solved efficiently in this paper. A CTtMIP query continuously monitors the t places with the maximum influence from the set of places, where the influence of a place is defined as the number of its bichromatic reverse k nearest neighbors (BRkNNs). Two new metrics and their corresponding rules are introduced to shrink the search region and reduce the candidates of BRkNNs checked. Extensive experiments confirm that our proposed approach outperforms the state-of-the-art competitor significantly.