In some mobile wireless sensor network applications, it is not necessary to monitor the entire field all the time, and only a number of critical points or points of interest (POIs) need to be monitored periodically. In this paper, we address the minimum-delay POIs coverage in mobile wireless sensor networks problem with cost restriction, which is how to schedule the limited number of mobile sensors monitoring to minimize the service delay of POIs. We study two scenarios of the problem. In the first scenario, the start positions of mobile sensors are determined in advance, we propose the SSR algorithm to address this problem. In the second scenario, without pre-defined start positions, we propose two algorithms, the TSP-S and the SSNOR. By the comprehensive simulations, we evaluate the performance of the proposed algorithms. The simulation results show the efficiency of our algorithms.