A novel hybrid model and simulation results for an advanced, graded base AlGaN/GaN heterojunction bipolar transistor structure are presented. The base of the n-p-n HBT examined has two parts, a linearly graded AlGaN layer on the emitter side and a heavily p-doped GaN layer on the collector side. In the hybrid model developed here the potential profile is first calculated self-consistently in the biased state taking into account ionized impurity charges, polarization charges, and majority carrier charges. The minority carrier transport is examined subsequently. Injection of electrons from the emitter is modeled as a thermionic emission process. The minority electron transport process in the graded region is drift-dominated due to the large built-in effective field strength. In the low-field GaN layer of the base, electron transport is assumed to be diffusion-dominated. High-level injection effects are modeled in the framework of the Gummel-Poon model. Example structure design parameters are presented and it is found that the calculated current gain can be greater than 25, with a collector current density of 10 4A/cm2.