One fundamental issue in application of wireless sensor networks is to provide proper coverage of their deployment regions, which answers the questions about the quality of service (surveillance or monitoring) that can be provided by a sensor network. In this paper, we consider the point-coverage problem where a given set of n points requires to be covered in the two-dimension (such as monitoring leakage of hazardous gaseous materials at ventilation points or observing the fixed location important targets). Our objective is to place the minimal number sensors such that coverage points in the field can be covered by at least k sensors. By combining Computational Geometry and Combinatorics techniques, we investigate the issue from a different angle, demonstrate an important relationship between coverage points and sensors, and develop an efficient algorithm for 1-coverage problem. Finally, we indicate our approach can easily solve k-coverage problem based on 1-coverage.