In this paper we present the results of the computer simulation of the GaSb-based multi-quantum-well GaInAsSb/GaSb vertical-cavity surface-emitting lasers (VCSELs) with the emission wavelength above 2.6 μm. Calculations have been performed with the aid of the comprehensive fully self-consistent numerical model developed by our group. The model combines electrical, thermal, gain, and optical effects, together with the mutual interactions between individual physical processes. For the selected active regions with various material contents and strains the influence of the ambient temperature and tunnel-junction diameter on continuous-wave performance characteristics has been taken into account. The results of the numerical analysis show that with the use of optimised active region it is possible to obtain stable single-fundamental-mode low-threshold operation of VCSEL with emission close to 2.8 μm. This wavelength is 0.2 μm longer than values reported so far for similar devices.