A new technique based on a vertical scanning white-light interferometry is developed for measuring fuel pressure in inertial confinement fusion (ICF) multiple-shell polymer-microsphere targets. Nuclear fuel pressure is an essential parameter for estimating fusion efficiency in ICF experiments. This parameter is difficult to determine because of complicated target structures, short measurement time, relatively short optical path length changes, and expansion of the target after pressurization. To reduce the effects due to changes in diameter, a model is proposed to correct for the expansion at the radial orientation for multiple-shell polymer microspheres. The model is compared to a destructive method, and D2 fill pressure accuracy is confirmed within a 10% error of uncertainty.