Graphene oxide has been synthesized by microwave-assisted exfoliation of graphite oxide prepared by modified Hummers method. Graphite was oxidized in a solution of $H_2O_2$ and $KMnO_4$ at $65{sim}80^{circ}C$, followed by 10 % $H_2O_2$ solution treatment at $80{sim}90^{circ}C$. The graphite oxide was exfoliated under microwave irradiation of 1 kW and was reduced to graphene effectively by hydrazine hydrate ($H_4N_2{cdot}H_2O$) treatment. The exfoliation of graphene oxide was significantly affected by the microwave irradiation on (heating)/off (cooling) period. An on/off period of 10 s/20 s resulted in much more effective exfoliation than that of 5 s/10 s with the same total treatment time of 10 min. This can be explained by the higher exfoliation temperature of 10 s/20 s. Repetition of the graphite oxidation and exfoliation processes also enhanced the exfoliation of graphene oxide. The thickness of the final graphene products was estimated to be several layers. The D band peaks of the Raman spectra of the final graphene products were quite low, suggesting a high crystal quality.