Histone deacetylases (HDAC) contain eighteen isoforms that can be divided into four classes. Of these isoform enzymes, class IIa (containing HDAC4, 5, 7 and 9) target unique substrates, some of which are client proteins associated with epigenetic control. Class IIa HDACs are reportedly associated with some neuronal disorders, making HDACs therapeutic targets for treating neurodegenerative diseases. Additionally, some reported HDAC inhibitors contain hydroxamate moiety that chelates with zinc ion to become the cofactor of HDAC enzymes. However, the hydroxamate functional group is shown to cause undesirable effects and has poor pharmacokinetic profile. This study used in silico virtual screening methodology to identify several nonhydroxamate compounds, obtained from National Cancer Institute database, which potentially inhibited HDAC4. Comparisons of the enzyme inhibitory activity against a panel of HDAC isoforms revealed these compounds had strong inhibitory activity against class IIa HDACs, but weak inhibitory activity against class I HDACs. Further analysis revealed that a single residue affects the cavity size between class I and class IIa HDACs, thus contributing to the selectivity of HDAC inhibitors discovered in this study. The discovery of these inhibitors presents the possibility of developing new therapeutic treatments that can circumvent the problems seen in traditional hydroxamate-based drugs.