With the advances of more and more mobile sink deployments (e.g., robots and unmanned aerial vehicles), mobile sinks have been demonstrated to play an important role in the prolongation of network lifetime. In this paper, we consider the network lifetime maximization problem for time-sensitive data gathering, which requires sensing data to be sent to the sink as soon as possible, subject to several constraints on the mobile sink. Because the mobile sink is powered by petrol or electricity, its maximum travel distance per tour is bounded. The mobile sink’s maximum moving distance from its current location to the next must also be bounded to minimize data loss. As building a new routing tree rooted at each new location will incur an overhead on energy consumption, the mobile sink must sojourn at each chosen location at least for a certain amount of time. The problem, thus, is to find an optimal sojourn tour for the mobile sink such that the network lifetime is maximized, which is subject to a set of constraints on the mobile sink: its maximum travel distance, the maximum distance of each movement, and the minimum sojourn time at each sojourn location. In this paper, we first formulate this novel multiple-constrained optimization problem as the distance-constrained mobile sink problem for time-sensitive data gathering. We then devise a novel heuristic for it. We finally conduct extensive experiments by simulation to evaluate the performance of the proposed algorithm. The experimental results demonstrate that the performance of the proposed algorithm is very promising, and the solution obtained is fractional of the optimal one. Copyright © 2011 John Wiley & Sons, Ltd.