Story listening in children relies on brain regions supporting speech perception, auditory word recognition, syntax, semantics, and discourse abilities, along with the ability to attend and process information (part of executive functions). Speed-of-processing is an early-developed executive function. We used functional and structural magnetic resonance imaging (MRI) to demonstrate the relationship between story listening and speed-of-processing in preschool-age children. Eighteen participants performed story-listening tasks during MRI scans. Functional and structural connectivity analysis was performed using the speed-of-processing scores as regressors. Activation in the superior frontal gyrus during story listening positively correlated with speed-of-processing scores. This region was functionally connected with the superior temporal gyrus, insula, and hippocampus. Fractional anisotropy in the inferior frontooccipital fasciculus, which connects the superior frontal and temporal gyri, was positively correlated with speed-of-processing scores. Our results suggest that speed-of-processing skills in preschool-age children are reflected in functional activation and connectivity during story listening and may act as a biomarker for future academic abilities.