Fluid intelligence has been associated with a distributed cognitive control or multiple-demand (MD) network, comprising regions of lateral frontal, insular, dorsomedial frontal, and parietal cortex. Human fluid intelligence is also intimately linked to task complexity, and the process of solving complex problems in a sequence of simpler, more focused parts. Here, a complex target detection task included multiple independent rules, applied one at a time in successive task epochs. Although only one rule was applied at a time, increasing task complexity (i.e., the number of rules) impaired performance in participants of lower fluid intelligence. Accompanying this loss of performance was reduced response to rule-critical events across the distributed MD network. The results link fluid intelligence and MD function to a process of attentional focus on the successive parts of complex behavior.SIGNIFICANCE STATEMENTFluid intelligence is intimately linked to the ability to structure complex problems in a sequence of simpler, more focused parts. We examine the basis for this link in the functions of a distributed frontoparietal or multiple-demand (MD) network. With increased task complexity, participants of lower fluid intelligence showed reduced responses to task-critical events. Reduced responses in the MD system were accompanied by impaired behavioral performance. Low fluid intelligence is linked to poor foregrounding of task-critical information across a distributed MD system.