Thanks to their formidable electron transport properties, III–V compound semiconductors have established themselves as a possible alternative to strained-Si as future n-type logic switches. To predict the performance of such transistors, device simulators that can capture the peculiarities of the III–V band structure at low computational cost are required. In particular, their strong band non-parabolicity (NP) calls for advanced models going beyond the standard effective mass approximation (EMA). Previous studies have suggested ways to include NP effects into quantum transport calculations in the ballistic limit. Here, such a model is extended to account for electron–phonon interactions. It combines the non-equilibrium Green’s function formalism and the EMA with NP corrections. The proposed method is validated through simulations of InGaAs nanowire field-effect transistors. The results are compared to full-band tight-binding calculations and to the solution of the subband Boltzmann transport equation, showing excellent agreement.