Network lifetime is a bottleneck that restricts the development of wireless sensor networks. One approach to save energy effectively and prolong network lifetime is to schedule some nodes to work and put other nodes into a low-powered sleep mode, while monitoring performance of network. The object of scheduling nodes is to obtain a minimum node set that can cover a monitored region. This is a NP-hard problem. Performances of present approximation algorithms have not been good. An approximation algorithm of a minimum cover set problem based on methodology is proposed. During the process of constructing a cover set, effective node that extends to maximal areas are selected to join the cover set. Theoretical analyses show that the algorithm can construct a cover set that perform well and has a time complexity that is O(n), where n is initial node number. Experimental results show that performance of this new algorithm outperform that of present algorithms. The size of a cover set is decreased by 14.2%. Also, execution time is less than that of present algorithms. When initial nodes are deployed densely, the average degree of coverage obtained by the algorithm is below 1.75 and has an approximation ratio below 1.45.