This manuscript describes a novel class of N-acylhydrazone (NAH) derivatives that act as histone deacetylase (HDAC) 6/8 dual inhibitors and were designed from the structure of trichostatin A (1). Para-substituted phenyl-hydroxamic acids presented a more potent inhibition of HDAC6/8 than their meta analogs. In addition, the effect of compounds (E)-4-((2-(4-(dimethylamino)benzoyl)hydrazono)methyl)-N-hydroxybenzamide (3c) and (E)-4-((2-(4-(dimethylamino)benzoyl)-2-methylhydrazono)methyl)-N-hydroxybenzamide (3f) on the acetylation of α-tubulin revealed an increased level of acetylation. These two compounds also affected cell migration, indicating their inhibition of HDAC6. An analysis of the antiproliferative activity of these compounds, which presented the most potent activity, showed that compound 3c induced cell cycle arrest and 3g induced apoptosis through caspase 3/7 activation. These results suggest HDAC6/8 as a potential target of future molecular therapies for cancer.