In this paper, we explore random dopant-induced threshold voltage fluctuations by directly solving quantum correction model for nanoscale metal-oxide-semiconductor field effect transistors (MOSFETs). To calculate the variance of the threshold voltage of nanoscale MOSFETs, quantum correction model at equilibrium conditions is expanded and numerically solved with perturbation and monotone iterative methods. Fluctuations of threshold voltage resulting from the random dopant, variations of gate oxide thickness and epitaxial layer, and the device width are calculated. Classical and quantum mechanical results are provided to support the conclusions drawn from the theoretical findings. In contrast to traditional quantum Monte Carlo approach and small signal analysis of the Schrödinger-Poisson equations, this approach shows good accuracy and computational efficiency, and is ready for industrial technology computer-aided design application.