Cancer stem cells (CSCs) are in general characterized by higher resistance to cell death and cancer therapies than non-stem differentiated cancer cells. However, we and others have recently revealed using glioma stem cells (GSCs) as a model that, unexpectedly, CSCs have specific vulnerabilities that make them more sensitive to certain drugs compared with their differentiated counterparts. We aimed in this study to discover novel drugs targeting such Achilles’ heels of GSCs as anti-GSC drug candidates to be used for the treatment of glioblastoma, the most therapy-resistant form of brain tumors. Here we report that domatinostat (4SC-202), a class I HDAC inhibitor, is one such candidate. At concentrations where it showed no or minimal growth inhibitory effect on differentiated GSCs and normal cells, domatinostat effectively inhibited the growth of GSCs mainly by inducing apoptosis. Furthermore, GSCs that survived domatinostat treatment lost their self-renewal capacity. These results suggested that domatinostat is a unique drug that selectively eliminates GSCs not only physically by inducing cell death but also functionally by inhibiting their self-renewal. Our findings also imply that class I HDACs and/or LSD1, another target of domatinostat, may possibly have a specific role in the maintenance of GSCs and therefore could be an attractive target in the development of anti-GSC therapies.