A quantum-mechanical compact model of the threshold voltage for quantum nanowire MOSFETs has been developed. This approach is based on analytical solutions for the decoupled 2D Schrödinger and 1D Poisson equations solved in the silicon channel. A quantum correction based on the perturbation theory has been also introduced to improve the model accuracy. Finally, the validity of the model has been verified by comparison with data obtained with a 2D/3D Poisson-Schrödinger drift-diffusion simulation code.