Normally-off AlGaN/GaN high electron mobility transistors (HEMTs) are indispensable devices for power electronics as they can greatly simplify circuit designs in a cost-effective way. In this work, the electrical characteristics of p-type InAlN gate normally-off AlGaN/GaN HEMTs with a step buffer layer of Al0.25Ga0.75N/Al0.1Ga0.9N is studied numerically. Our device simulation shows that a p-InAlN gate with a step buffer layer allows the transistor to possess normally-off behavior with high drain current and high breakdown voltage simultaneously. The gate modulation by the p-InAlN gate and the induced holes appearing beneath the gate at the GaN/Al0.25Ga0.75N interface is because a hole appearing in the p-InAlN layer can effectively vary the threshold voltage positively. The estimated threshold voltage of the normally-off HEMTs explored is 2.5 V at a drain bias of 25 V, which is 220% higher than the conventional p-AlGaN normally-off AlGaN/GaN gate injection transistor (GIT). Concurrently, the maximum current density of the explored HEMT at a drain bias of 10 V slightly decreases by about 7% (from 240 to 223 mA mm-1). At a drain bias of 15 V, the current density reached 263 mA mm-1. The explored structure is promising owing to tunable positive threshold voltage and the maintenance of similar current density; notably, its breakdown voltage significantly increases by 36% (from 800 V, GIT, to 1086 V). The engineering findings of this study indicate that novel p-InAlN for both the gate and the step buffer layer can feature a high threshold voltage, large current density and high operating voltage for advanced AlGaN/GaN HEMT devices.