When mobile sensors are initially deployed, some sensors may be located far away from the region of interest and due to the sensor's limited sensing of range, some sensors may not be able to participate in the coverage task. This paper proposes a new algorithm on the coverage problem for mobile sensor networks which guarantees all sensors to participate in the coverage task. The algorithm is a combination of the standard gradient-based coverage algorithm and leader-following algorithm and is designed to maximize the joint detection probabilities of the events in the region of interest. First, leader sensors are selected based on the information which each sensor has gathered. The rest of the sensors will follow the leaders until they have sufficient information on the region of interest and then switch to the standard coverage algorithm. The proposed algorithm can be performed in a distributed manner. Moreover, the proposed algorithm could also improve the convergence speed of the coverage task. The results are validated through numerical simulations.