Several hydroxamic acid derivatives with a substituted phthalimide group as a linker and/or cap structure, prepared during structural development studies based on thalidomide, were found to have histone deacetylase (HDAC)-inhibitory activity. Structure-activity relationship studies indicated that nature of the substituent introduced at the phthalimide nitrogen atom, introduction of a hydroxamic acid structure, and distance between the N-hydroxyl group and the cap structure are important for HDAC-inhibitory activity.