The exceptional properties of the two-dimensional material, graphene, having high-mobility carriers, deployable on a large area have made it attractive for RF electronic applications. However, the channel mobility in graphene-channel field effect transistors (GFET) is still limited by various external scattering sources and the absence of a bandgap in graphene causes poor current on-off ratio and unsatisfying current saturation in GFETs. Graphene-base hot-electron transistor (GB-HET) uses the single-atomic thick, semi-metallic graphene as the base region of the hot-electron transistor. It provides an alternative way to utilize the unique properties of graphene and solve some problems of the GFETs based on a different operational principle. This dissertation focuses the operational principle, fabrication and characterization of several types of GB-HETs. Current saturation with high current on-off ratio are observed in the current-voltage characteristics of GB-HETs. The influence of the tunnel barrier, filter barrier and emitter/collector area ratio on the common-base current gain of GB-HET are investigated. The current gain is improved by more than two orders of magnitude by optimizing these device parameters. The results suggest that the quality and choice of the materials are key elements for the implementation of GB-HETs into practical applications. In addition, theoretical studies show that phonon scattering in the dielectrics and reflections at the interfaces may reduce the energy of the hot electrons and suppress the transmission probability, and thus limit the maximum current gain of GB-HETs. Developing mature process, accurate physical models, involving new materials and experiment methods, as well as having a better fundamental understanding of the electron transport in the direction perpendicular to the graphene sheet, are highly desirable to reveal the ultimate performance of GB-HETs for high-speed electronics.