Different cognitively demanding tasks recruit globally distributed but functionally specific networks. However, the configuration of core networks and their reconfiguration patterns across cognitive loads remain unclear, as does whether these patterns are indicators for the performance of cognitive tasks. In this study, we analyzed functional magnetic resonance imaging data of a large cohort of 448 subjects, acquired with the brain at resting state and executing N-back working memory (WM) tasks. We discriminated core networks by functional interaction strength and connection flexibility. Results demonstrated that the frontoparietal network (FPN) and default mode network (DMN) were core networks, but each exhibited different patterns across cognitive loads. The FPN and DMN both showed strengthened internal connections at the low demand state (0-back) compared with the resting state (control level); whereas, from the low (0-back) to high demand state (2-back), some connections to the FPN weakened and were rewired to the DMN (whose connections all remained strong). Of note, more intensive reconfiguration of both the whole brain and core networks (but no other networks) across load levels indicated relatively poor cognitive performance. Collectively these findings indicate that the FPN and DMN have distinct roles and reconfiguration patterns across cognitively demanding loads. This study advances our understanding of the core networks and their reconfiguration patterns across cognitive loads and provides a new feature to evaluate and predict cognitive capability (e.g., WM performance) based on brain networks.