In this paper, we present a fabrication process of graphene field effect transistors (GFETs) using natural oxidation of aluminum as dielectrics, which provide an alternative fabrication choice for future flexible electronics with the large scale and arbitrary substrates. The high-quality monolayer graphene is preserved by our process, and the mobility up to 3250 cm2/Vs is measured after whole device fabrication. GFETs with double bottom-gate structure varying from 300 to 100 nm in gate length have been characterized by both static and dynamic measurements. The total gate capacitances of our device structure are evaluated based on the measurement results of scattering parameters. We report an intrinsic current gain cutoff frequency of 11 GHz and a maximum oscillation frequency of 8 GHz in devices with 100 nm gate length. Moreover, both the values of and for different gate lengths are also discussed. Our results indicate that the full process exhibits great potential, especially for graphene-based flexible electronics.