Cognitive control resolves conflict between task-relevant and -irrelevant information to enable goal-directed behavior. As conflict can arise from different sources (e.g., sensory input, internal representations), how a finite set of cognitive control processes can effectively address huge array of conflict remains a major challenge. We hypothesize that different conflict can be parameterized and represented as distinct points in a (low-dimensional) cognitive space, which can then be resolved by a limited set of cognitive control processes working along the dimensions. To test this hypothesis, we designed a task with five types of conflict that could be conceptually parameterized along one dimension. Over two experiments, both human performance and fMRI activity patterns in the right dorsolateral prefrontal (dlPFC) support that different types of conflict are organized in a cognitive space. The findings suggest that cognitive space can be a dimension reduction tool to effectively organize neural representations of conflict for cognitive control.