The aim of this study was to explore whether there are networks of regions where maturation of white matter and changes in brain activity show similar developmental trends during childhood. In a previous study, we showed that during childhood, grey matter activity increases in frontal and parietal regions. We hypothesized that this would be mediated by maturation of white matter. Twenty-three healthy children aged 8-18 years were investigated. Brain activity was measured using the blood oxygen level-dependent (BOLD) contrast with functional magnetic resonance imaging (fMRI) during performance of a working memory (WM) task. White matter microstructure was investigated using diffusion tensor imaging (DTI). Based on the DTI data, we calculated fractional anisotropy (FA), an indicator of myelination and axon thickness. Prior to scanning, WM score was evaluated. WM score correlated independently with FA values and BOLD response in several regions. FA values and BOLD response were extracted for each subject from the peak voxels of these regions. The FA values were used as covariates in an additional BOLD analysis to find brain regions where FA values and BOLD response correlated. Conversely, the BOLD response values were used as covariates in an additional FA analysis. In several cortical and sub-cortical regions, there were positive correlations between maturation of white matter and increased brain activity. Specifically, and consistent with our hypothesis, we found that FA values in fronto-parietal white matter correlated with BOLD response in closely located grey matter in the superior frontal sulcus and inferior parietal lobe, areas that could form a functional network underlying working memory function.