Hyperspectral imaging is used in various fields because it can obtain much more information than imaging by conventional RGB cameras. Hyperspectral imaging systems using active illumination, prisms, gratings, or narrowband filters have been proposed. Active illumination systems can obtain two-dimensional (2D) spectral images rapidly, and the device can be low-cost and small because of the use of LEDs. However, flicker can occur when different colors of LEDs are switched. The other methods do not have the flicker problem because they use passive imaging. However, these systems take a long time to acquire the 2D spectral images, or they tend to be high-cost or large. In our research, we propose a flickerless active LED illumination system for hyperspectral imaging. This system acquires images while switching the illumination. The switching illumination consists of many narrowband LEDs that have different spectrums. The spectral images of each LED are reconstructed from the acquired images. The switching illumination is designed to reduce the flicker based on human visual characteristics. We reduce the color changes of the switching illumination while maintaining its spectral differences. In the experiment, we obtain the optimal design of a flickerless illumination system for measuring oxygen saturation. To show the feasibility of our system, we clearly show the difference in saturation using the spectral images obtained by a prototype designed using the proposed method.