Cross-efficiency　evaluation　is　an　effective　method　for　ranking　decision　making　units　(DMUs)　in　data　envelopment　analysis,　which　is　performed　with　peer-evaluation　and　self-evaluation.　From　different　points　of　view,　various　cross-efficiency　evaluations　have　been　proposed　with　different　secondary　goals.　Yet　they　usually　lead　to　different　average　cross-efficiencies　and　different　rankings.　In　this　paper,　we　develop　a　concept　of　the　aggressive　game　cross-efficiency,　and　propose　an　aggressive　secondary　model　to　minimize　the　cross-efficiencies　of　other　DMUs　under　the　constraints　that　the　aggressive　game　cross-efficiency　of　the　evaluated　DMU　is　guaranteed.　To　achieve　the　aggressive　game　cross-efficiency,　we　develop　an　iterative　algorithm.　Mathematically,　it　is　proved　that　all　conventional　average　cross-efficiencies　are　sure　to　converge　to　the　same　aggressive　game　cross-efficiency　by　the　iterative　algorithm.　Finally,　numerical　examples　are　presented　to　show　the　effectiveness　of　our　approach　in　evaluating　and　ranking　DMUs.　©　2017,　Springer　Science+Business　Media　New　York.