In wireless sensor networks, the area coverage sensing technology is the one of the key foundation technologies. IT is concerned about how to prolong the network lifetime based on meeting user sensing demands. Among the study of area coverage sensing technology, localized area coverage algorithm is gradually attracting wide attention for its less traffic and lower single-node computation. At present, the existing localized area coverage algorithms mainly depends on connectivity critical condition proposed by Xing. This condition is concerned about how to improve the perceived quality to coverage full area, ignores further studying for the network node connectivity. So, this connectivity condition is from the perspective of single node connectivity, resulting in limited conditions for algorithm application. For above issues, firstly, the coverage node set connectivity is introduced for localized area coverage algorithm in this paper. Secondly, the loose connectivity critical condition to ensure coverage and connectivity is re-analyzed from the perspective of network connectivity. Finally, a circle intersection localized coverage algorithm under different conditions to maintain connectivity is designed, to extend the application scene. Simulation results show that the algorithm, under different conditions, can maintain network node connectivity on the basis of ensuring full area coverage.