Due to a growing demand for a viable label-free observation method in the biomedical field, many techniques, such as quantitative phase imaging and Raman spectroscopy, have been studied, and a complementary approach, hyperspectral imaging, has also been introduced. We developed a high-speed hyperspectral imaging microscopy imaging method with commercially available apparatus, employing a liquid crystal tunable bandpass filter combined with a pixel-wise machine learning classification. Next, we evaluated the feasibility of the application of this method for stem cell research utilizing neural stem cells. Employing this microscopy method, with a 562 × 562 μm2 field of view, 2048 × 2048 pixel resolution images containing 63 wavelength pixel-wise spectra could be obtained in 30 seconds. The neural stem cells were differentiated into neurons and astroglia (glia), and a four-class cell classification evaluation (including neuronal cell body, glial cell body, process and extracellular region) was conducted under co-cultured conditions. As a result, an average of 88% of the objects of interest were correctly classified, with an average precision of 94%, and more than 99% of the extracellular pixels were correctly segregated. These results indicated that the proposed hyperspectral imaging microscopy is feasible as a label-free observation method for stem cell research.