The dependence of the interband tunneling current on AlSb barrier widths is studied in the InAs/AlSb/GaSb single-barrier diode structures. The experimental results show that the peak current density displays an exponential dependence on the barrier width. The Wentzel-Kramers-Brillouin approximation combined with the k̇p two-band model were used in analyzing the energy level in the AlSb barrier through which the peak tunneling currents occur. The energy level thus obtained (0.48±0.10 eV above the valence band edge of the AlSb) agrees with the valence-band offset (0.40±0.15 eV) between the AlSb and the GaSb obtained by x-ray photoemission measurement reported by Gualtieri et al. [Appl. Phys. Lett. 49, 1037 (1986)]. By adjusting the barrier width properly, we obtained a high peak current density of 24 kA/cm2 (with a peak-to-valley ratio of 1.4) and a high peak-to-valley ratio of 4.5 (with a peak current density of 3.5 kA/cm2) at room temperature. In addition, the peak-current voltages for different AlSb barrier widths were calculated and compared with the measured results.