Electrospinning is a simple versatile process used to produce nanofibers and collect them as a nanofiber mat. However, due to bending instability, electrospinning often produces a nanofiber mat with non-uniform mat thickness. In this study, we developed a uniform-thickness electrospun nanofiber mat (UTEN) production system with a movable collector based on real-time thickness measurement and thickness feedback control. This system is compatible with a collector with void regions such as a mesh-type collector, two-parallel-metal-plate collector, and ring-type collector, which facilitates the measurement of light transmittance across the produced nanofiber mat during electrospinning. A real-time measurement system was developed to measure light transmittance and convert it to the thickness of the nanofiber mat in real time using the Beer-Lambert law. Thickness feedback control was achieved by repeating the following sequences: (1) finding an optimal position of the movable collector based on the measured thickness of the nanofiber mat, (2) shifting the collector to an optimal position, and (3) performing electrospinning for a given time step. We found that the suggested thickness feedback control algorithm could significantly decrease the non-uniformity of the nanofiber mat by reducing the standard deviation by more than 8 and 3 times for the numerical simulation and experiments, respectively, when compared with the conventional electrospinning. As a pioneering research, this study will contribute to the development of an electrospinning system to produce robust and reliable nanofiber mats in many research and industrial fields such as biomedicine, environment, and energy.