To improve the performance of the conventional p-GaN gate AlGaN/GaN high electron mobility transistors (HEMTs), we propose an improved design for e-mode AlGaN/GaN HEMT with a gate stack β-Ga2O3/p-GaN structure. The simulated results show that the proposed device increases the threshold voltage and the gate breakdown voltage in comparison with the conventional p-GaN gate HEMT due to the use of the β-Ga2O3 layer, which has an additional β-Ga2O3/p-GaN heterojunction and decreases the strength of electric field in the gate region. Moreover, the proposed device exhibits a lower off-state leakage current, which can be attributed to the less donor ionized density. In addition, the impacts of the β-Ga2O3 layer thickness are investigated. There is a trade-off between β-Ga2O3 layer thickness and the performance of the proposed device, including threshold voltage, gate breakdown, and saturation drain current.