We report on the role of AlSb material in the reduction of threading dislocation density (TDD) in the GaSb/AlSb/GaAs system. The AlSb layers were grown using low-temperature (LT) MBE, exploiting the interfacial misfit (IMF) dislocation array. AlSb layers with four different thicknesses in the range of 1–30 nm were investigated. The results showed the inhibiting role of LT-AlSb layers in the reduction of TDD. Values of TDD as low as 2.2 × 106 and 6.3 × 106 cm−2 for samples with thin and thick AlSb layers were obtained, respectively. The filtering role of AlSb material was proven despite the IMF-AlSb/GaAs interface’s imperfectness caused by the disturbance of a 90° dislocation periodic array by, most likely, 60° dislocations. The dislocation lines confined to the region of AlSb material were visible in HRTEM images. The highest crystal quality and smoother surface of 1.0 μm GaSb material were obtained using 9 nm thick AlSb interlayer. Unexpectedly, the comparative analysis of the results obtained for the GaSb/LT-AlSb/GaAs heterostructure and our best results for the GaSb/GaAs system showed that the latter can achieve both higher crystal quality and lower dislocation density.