In the present paper, a comprehensive computer simulation is used to determine optimal structure of the InPbased GaInNAs quantum-well (QW) active region and to investigate a possibility of reaching room-temperature (RT) continuous-wave (CW) single-fundamental-mode 2.33-µm operation of vertical-cavity surface-emitting laser (VCSEL) with such an active region. From among various considered InP-based active regions, the one with the Ga 0.15 In 0.85 N 0.015 As 0.985 /Al 0.138 Ga 0.332 In 0.530 As QW, i.e. with barriers lattice matched to InP, seems to be optimal for the 2.33-µm VCSEL performance. Its QW material is chosen for the required long-wavelength emission whereas its barrier is expected to ensure promising laser performance at room and higher temperatures. The latter is mostly connected with the QW conduction band offset equal in the above active region to as much as 413 meV, which is much larger than those of its possible lattice matched to InP competitors, e.g. 276 meV for the Ga 0.47 In 0.53 As barrier and 346 meV for the Ga 0.327 In 0.673 As 0.71 P 0.29 one. Our simulation reveals that from among various considered structures, a VC-SEL with a 4-µm-diameter tunnel junction and two 6-nm Ga 0.15 In 0.85 N 0.015 As 0.985 /Al 0.138 Ga 0.332 In 0.530 As QWs exhibits the lowest calculated threshold current of 0.88 mA. Its promising RT CW performance suggests that it may represent a very interesting alternative to GaSb-based VCSELs.