The target coverage problem in wireless sensor networks is concerned with maximizing the lifetime of the network while continuously monitoring a set of targets. We add a QoS requirement to the target coverage such that the targets are covered by more than one sensor at any time. Given an integer vector Q, where q _i is the minimum number of sensors to simultaneously cover targets i, the problem becomes Q-coverage problem. In this paper, we study the target Q-coverage problem. The objective is to maximize sensor network lifetime satisfying Q-coverage requirement. The problem is shown to be NP-complete and there is no known practical algorithm. We propose a heuristic and show that the proposed algorithm yields solution very near to the optimal solution. Our algorithm has two important features. It uses a greedy heuristic to generate Q-covers by prioritizing sensors in terms of the residual battery life and the algorithm assigns a small constant of lifetime to Q-covers so generated. In this process, it allows the sensors to participate in many Q-covers. We observe that the smaller the constant, the closer is the solution to optimal solution. Through experiments on randomly generated problem instances, we show that the proposed algorithm yields near-optimal solution.