The high-frequency performance of top-gated graphene field-effect transistors (GFETs) depends to a large extent on the saturation velocity of the charge carriers, a velocity limited by inelastic scattering by surface optical phonons from the dielectrics surrounding the channel. In this work, we show that, by simply changing the graphene channel surrounding dielectric with a material having higher optical phonon energy, one could improve the transit frequency and maximum frequency of oscillation of GFETs. We fabricated GFETs on conventional SiO2/Si substrates by adding a thin Al2O3 interfacial buffer layer on top of SiO2/Si substrates, a material with about 30% higher optical phonon energy than that of SiO2, and compared performance with that of GFETs fabricated without adding the interfacial layer. From S-parameter measurements, a transit frequency and a maximum frequency of oscillation of 43 and 46 GHz, respectively, were obtained for GFETs on Al2O3 with 0.5- $\mu \text{m}$ gate length. These values are approximately 30% higher than those for state-of-the-art GFETs of the same gate length on SiO2. For relating the improvement of GFET high-frequency performance to improvements in the charge carrier saturation velocity, we used standard methods to extract the charge carrier velocity from the channel transit time. A comparison between two sets of GFETs with and without the interfacial Al2O3 layer showed that the charge carrier saturation velocity had increased from $1.5\cdot 10^{{7}}$ to $2\cdot 10^{{7}}$ cm/s.