Reading learning disability (RLD) is characterized by a specific difficulty in learning to read that is not better explained by an intellectual disability, lack of instruction, psychosocial adversity, or a neurological disorder. According to the domain-general hypothesis, a working memory deficit is the primary problem. Working memory in this population has recently been linked to altered resting-state functional connectivity within the default mode network (DMN), salience network (SN), and frontoparietal network (FPN) compared to that in typically developing individuals. The main purpose of the present study was to compare the within-network functional connectivity of the DMN, SN, FPN, and reading network in two groups of children with RLD: a group with lower-than-average working memory (LWM) and a group with average working memory (AWM). All subjects underwent resting-state functional magnetic resonance imaging (fMRI), and data were analyzed from a network perspective using the network brain statistics framework. The results showed that the LWM group had significantly weaker connectivity in a network that involved brain regions in the DMN, SN, and FPN than the AWM group. Although there was no significant difference between groups in reading network in the present study, other studies have shown relationship of the connectivity of the angular gyrus, supramarginal gyrus, and inferior parietal lobe with the phonological process of reading. The results suggest that although there are significant differences in functional connectivity in the associated networks between children with LWM and AWM, the distinctive cognitive profile has no specific effect on the reading network.