The influences of the hole-doped and biaxial strain applied on the electronic structure and magnetism of graphene-like ZnO monolayer are systematically investigated by the first-principles calculations. The results show that hole-doped ZnO monolayer transits from nonmagnetic state to magnetic state once the hole density reaches a certain value (3.65 x 10(14) cm(-2)), and the average spin magnetic moment increases by 1.0 mu(B)/hole upon increasing the hole density from 0.3 x 10(14) to 8.2 x 10(14) cm(-2). More interestingly, the critical hole density can be effectively reduced by applying the biaxial strain. The magnetism of hole-doping ZnO monolayer with biaxial strain comes from the O-p(z) states. Our study demonstrates that the combined effect of the hole doping and biaxial strain on ZnO monolayer can modulate its electronic and magnetic properties, which can be applied in nanoelectronics and spintronics.