Directional sensor networks have a lot of practical applications, and target coverage is one of the most important issues. In this article, we study the target coverage problem in directional sensor network, where directional sensors can rotate freely around their centers and targets are attached with differentiated coverage quality requirements. Our goal is to maximize the lifetime of sensor network, satisfying the coverage quality requirements of all targets. We model it as the maximum cover sets problem and address it by organizing the directions of sensors into a group of non-disjoint cover sets, which can cover all targets, satisfying their coverage quality requirements, and then schedule them alternately to extend the network lifetime. It consists of two parts. First, since directional sensor has infinite directions by rotating continuously, we propose sensing direction partition algorithm to find all non-redundancy directions for each sensor according to the targets deployed within the sensing region of the sensor. Then, based on the result of the sensing direction partition algorithm, we propose an efficient heuristic algorithm for the maximum cover sets problem to organize the directions of sensors into a number of non-disjoint cover sets and allocate work time for each cover set. Besides, we get an upper bound of the optimal solution for the problem. Finally, simulation results are presented to demonstrate the performance of our algorithm.