High-efficiency dielectrics are promising materials that may enable nanoelectronic devices, such as carbon nanotubes and graphene transistors, to reach their performance limits. A high current on/off ratio, low voltage operation, high on-current and current saturation were all realized in a chemical vapor deposition graphene transistor by using a high-efficiency ion-gel dielectric. Using a drift–diffusion device model based on the surface potential in the channel that also considers the contact resistance at the channel boundary, the output characteristics of the graphene transistor are simulated, which agrees well with the experimental data and indicates that the current saturation in the graphene channel is intrinsic ambipolar performance under low field conditions. We also demonstrate an ambipolar invertor based on these high performance graphene transistors with gain values as high as 4.