Abstract: The magnetism and the electronic structure of transition metal TM co-doped II-VI compound-based diluted magnetic semiconductors（DMSs） are investigated based on Ab-initio calculations.The stability of the ferromagnetic state in ZnO-based DMSs is investigated systematically and materials design for ferromagnetic DMSs is given.In all host materials,it is found that（Mn,Co）,（Co,Ni） and（Mn,Ni） co-doped systems are ferromagnetic,while（Fe,Ni） co-doped systems are spin-glass state.On the other hand,for Fe-,Co-and Ni-doped systems,the ferromagnetic state is stable in ZnO-based DMS.The carrier-induced ferromagnetism in ZnO-based DMSs is also investigated and it is found that their magnetic states are controllable by changing the carrier density.Analyzing the calculated density of states,the mechanism to stabilize the ferromagnetic state in the DMSs is discussed.And the magnetism can be explained by double exchange and super-exchange theories.