In this work results of the computer simulation of semiconductor-based vertical-cavity surface-emitting lasers with GaInAsSb/GaSb active region and emission in the 2.6–2.8 μm wavelength range obtained with the use of comprehensive fully self-consistent optical-electrical-thermal -recombination numerical model have been presented. The resulting calculations showed that with the increasing emission wavelength the stable fundamental mode operation becomes more difficult to achieve due to reduction of the temperature operation range. Furthermore, the range of the lateral dimensions of the tunnel junction for which the LP01 mode operation can be obtained is also decreased. In the case of laser designed for 2.7-μm operation, using the tunnel junction with diameter wider than 4 μm leads to the situation when the LP11 mode is the preferred one. For the emission wavelength around 2.8 μm, the LP01 mode operation is limitted only to devices with tunnel junction with diameter equal to 2 μm.