In order to maximize the lifetime of wireless sensor network（WSN）, a lifetime maximization strategy to ensure coverage and connectivity in WSN is proposed in this paper. First of all, the problem is considered as an energysaving coverage problem and formulated using integer linear programming technique, and a feasible set containing the minimum number of sensors is obtained. These feasible sets cover all the target points and have the largest sum of utility at the same time. Secondly, in order to ensure each feasible set has the coverage and connectivity of the network, the energysaving coverage problem is extended to a lifetime coverage and connectivity problem. A greedy iterative heuristic algorithm, which is composed of coverage phase, connectivity phase and redundant sensor reduction phase, is used to solve this problem in order to find the maximum number of disjoint active (feasible) sets and to activate them successively. Thus, the extended network lifetime R is obtained. Experimental results show that the proposed algorithm is very close to the optimal solution in terms of network lifetime and energy efficiency performance, and the network lifetime is linearly related to the number of sensor nodes in WSN.