To reduce the leakage current of InAs/AlSb HEMTs, deposition of a high-k dielectric is required between the InAlAs protection layer and the gate electrode to form a metal-oxide-semiconductor capacitor insulated gate. In this paper, two kinds of high-k/n-InAlAs MOS-capacitors with HfO2 and HfAlO dielectric, respectively, were successfully fabricated. Both devices presented a low leakage current density of 10(-9)-10(-4) A/cm(2) under the bias voltage range from -5V to 5V. A Space-charge-limited conduction was observed at a low bias condition, Schottky emission and Frenkel-Poole emission mechanisms began to dominate when voltage was increased, and Fowler-Nordheim tunneling occurred at high fields for both devices. Compared with the HfO2/n-InAlAs MOS-capacitor, the extracted barrier height phi(B) and conduction band offset Delta E-cB of the HfAlO/n-InAlAs MOS-capacitor were clearly higher, this effect resulted in HfAlO/n-InAlAs MOS-capacitor presenting a lower leakage current density. It is demonstrated that HfAlO deposited on InAlAs can suppress the leakage current more effectively than HfO2, which suggests good potential for applications of HfAlO/n-InAlAs MOS-capacitors as the insulated-gate of InAs/AlSb high-electron-mobility transistors.