Based　on　the　coverage　relationship　between　sensors　and　targets　in　wireless　sensor　networks　with　adjustable　sensing　ranges,　a　lifetime　evaluation　approach　for　targets　is　presented.　Considering　that　the　network　lifetime　depends　on　the　target　with　minimum　lifetime,　this　paper　proposes　two　methods　to　prolong　the　minimum　lifetime　of　targets　based　on　the　analysis　of　the　influence　of　the　change　of　sensing　ranges,　models　the　target　coverage　problem　using　a　game　theoretic　paradigm　and　proves　the　existent　of　a　pure　strategic　Nash　Equilibrium.　We　designs　a　distributed　algorithm　(called　DATC)　for　target　coverage.　In　DATC,　according　to　the　energy　of　neighbors　and　the　coverage　of　targets,　each　sensor　chooses　the　best　sensing　range　to　ensure　full　coverage　and　prolong　the　minimum　lifetime　of　targets.　Simulation　results　show　that　DATC　can　prolong　the　network　lifetime　effectively　in　different　network　scenarios.