In this paper, Capacitance-Voltage (CV) characteristics and direct tunneling gate leakage performance of InAs/AlSb Metal Oxide Semiconductor High Electron Mobility Transistor (MOS-HEMT) are investigated. 1-D coupled Schrӧdinger-Poisson equations are solved for electrostatic characterization of InAs/AlSb MOS-HEMT considering wave function penetration and strain effects. Using modified Wentzel–Kramers–Brillouin (WKB) method for transmission probability, direct tunneling gate leakage current is also calculated for the MOS-HEMT structure. Dependence of CV characteristics and direct tunneling gate leakage current on some important process and physical parameters such as oxide thickness, channel thickness, capping layer composition, gate dielectric material, doping concentration of delta layer and temperature are studied in this work. Our simulation results agree the pattern of variation with the experimental results reported by H. K. Lin et al.