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This paper investigates a covering time minimization problem of the maritime rescue missions that arise in practical rescue operations in the context of Hong Kong waters. In this problem, a fleet of heterogeneous vessels is deployed at marine police bases to deal with emergencies.Once an emergency rescue request is received, the marine police should send sufficient vessels to arrive at the incident site as soon as possible to provide critical medical service to the injured or the sick and then transport patients to emergency medical facilities. A basic question to the rescue missions is that what is the minimal covering time that marine police could promise to arrive at any incident site in its responsible water district. The shorter time the water district can be covered, the more likely lives and properties can be saved and the better the rescue service is. To address this problem, this paper formulates a mixed-integer programming model.Considering the expensive computational effort associated with solving this model, a two-stage method is proposed. Extensive numerical experiments and a case study are performed to demonstrate the efficiency of the proposed algorithm and illustrate how our model can be applied to solve practical problems. Our study contributes to the stream of research on maritime rescue problem that is gaining increasing concern in recent years. The proposed method can help rescue agency to provide faster response to rescue missions.