In this work results of a threshold operation of antimonide-based tunnel-junction (TJ) VCSEL have been presented with the aid of the comprehensive fully self-consistent optical-electrical-thermal-recombination numerical model. Calculations have been carried out for the structure with GaInAsSb/GaSb active region emitting at 2.6 μm. In order to suppress higher-order transverse modes in the device three different methods have been used. It has been shown that each of these methods allows us to achieve lasing with the LP01 mode for structure with TJ diameter of 8 μm, which has not been possible for the structure without modifications. Although using these methods leads to higher values of the threshold current, the drop of the maximal operating temperature for the structure with TJ diameter of 7 μm has not been higher than 10 K.