Allocating attentional resources to currently relevant information in a dynamically changing environment is critical to goal-directed behavior. Previous studies in nonhuman primates (NHPs) have demonstrated modulation of neural representations of stimuli, in particular visual categorizations, by behavioral significance in the lateral prefrontal cortex. In the human brain, a network of frontal and parietal regions, the "multiple demand" (MD) system, is involved in cognitive and attentional control. To test for the effect of behavioral significance on categorical discrimination in the MD system in humans, we adapted a previously used task in the NHP and used multivoxel pattern analysis for fMRI data. In a cued-detection categorization task, participants detected whether an image from one of two target visual categories was present in a display. Our results revealed that categorical discrimination is modulated by behavioral relevance, as measured by the distributed pattern of response across the MD network. Distinctions between categories with different behavioral status (e.g., a target and a nontarget) were significantly discriminated. Category distinctions that were not behaviorally relevant (e.g., between two targets) were not discriminated. Other aspects of the task that were orthogonal to the behavioral decision did not modulate categorical discrimination. In a high visual region, the lateral occipital complex, modulation by behavioral relevance was evident in its posterior subregion but not in the anterior subregion. The results are consistent with the view of the MD system as involved in top-down attentional and cognitive control by selective coding of task-relevant discriminations. Significance statement: Control of cognitive demands fundamentally involves flexible allocation of attentional resources depending on a current behavioral context. Essential to such a mechanism is the ability to select currently relevant information and at the same time filter out information that is irrelevant. In an fMRI study, we measured distributed patterns of activity for objects from different visual categories while manipulating the behavioral relevance of the categorical distinctions. In a network of frontal and parietal cortical regions, the multiple-demand (MD) network, patterns reflected category distinctions that were relevant to behavior. Patterns could not be used to make task-irrelevant category distinctions. These findings demonstrate the ability of the MD network to implement complex goal-directed behavior by focused attention.