We demonstrate vertical graphene-base hot-electron transistors (GB-HETs) with a variety of structures and material parameters. Our GB-HETs exhibit a current saturation with a high current on-off ratio (>10(5)), which results from both the vertical transport of hot electrons across the ultrathin graphene base and the filtering of hot electrons through a built-in energy barrier. The influences of the materials and their thicknesses used for the tunneling and filtering barriers on the common-base current gain α are studied. The optimization of the SiO2 thickness and using HfO2 as the filtering barrier significantly improves the common-base current gain α by more than 2 orders of magnitude. The results demonstrate that GB-HETs have a great potential for high-frequency, high-speed, and high-density integrated circuits.