Magnetic ZnO, one of the most important diluted magnetic semiconductors (DMS), has attracted great scientific interest because of its possible technological applications in optomagnetic devices. Magnetism in this material is usually delicately tuned by the doping level, dislocations, and local structures. The rational control of magnetism in ZnO is a highly attractive approach for practical applications. Here, the tuning effect of biaxial strain on the d(0) magnetism of native imperfect ZnO is demonstrated through first-principles calculations. Our calculation results show that strain conditions have little effect on the defect formation energy of Zn and O vacancies in ZnO, but they do affect the magnetism significantly. For a cation vacancy, increasing the compressive strain will obviously decrease its magnetic moment, while tensile strain cannot change the moment, which remains constant at 2 mu(B). For a singly charged anion vacancy, however, the dependence of the magnetic moment on strain is opposite to that of the Zn vacancy. Furthermore, the ferromagnetic state is always present, irrespective of the strain type, for ZnO with two zinc vacancies, 2V(Zn)s. A large tensile strain is favorable for improving the Curie temperature and realizing room temperature ferromagnetism for ZnO-based native semiconductors. For ZnO with two singly charged oxygen vacancies, 2V(O)(+)s, no ferromagnetic ordering can be observed. Our work points the way to the rational design of materials beyond ZnO with novel non-intrinsic functionality by simply tuning the strain in a thin film form.