The neural representation of concepts is a focus of many cognitive neuroscience studies. Prior works studying concept representation with neural imaging data have been largely limited to concrete concepts. The use of relatively small and constrained sets of stimuli leaves open the question of whether the findings can generalize other concepts. We share an fMRI dataset in which 11 participants thought of 672 individual concepts, including both concrete and abstract concepts. The concepts were probed using words paired with images in which the words were selected to cover a wide range of semantic categories. Furthermore, according to the componential theories of concept representation, we collected the 54 semantic features of the 672 concepts comprising sensory, motor, spatial, temporal, affective, social, and cognitive experiences by crowdsourcing annotations. The quality assessment results verify this as a high-quality neuroimaging dataset. Such a dataset is well suited to study how the brain represents different semantic features and concepts, creating the essential condition to investigate the neural representation of individual concepts.