Executive functions, the set of cognitive control processes that facilitate adaptive thoughts and actions, are composed primarily of three distinct yet interrelated cognitive components: Inhibition, Shifting, and Updating. While prior research has examined the nature of different components as well as their inter-relationships, fewer studies examined whole-brain connectivity to predict individual differences for the three cognitive components and associated tasks. Here, using the Connectome-based Predictive Modelling (CPM) approach and open-access data from the Human Connectome Project, we built brain network models to successfully predict individual performance differences on the Flanker task, the Dimensional Change Card Sort task, and the 2-back task, each putatively corresponding to Inhibition, Shifting, and Updating. We focused on grayordinate fMRI data collected during the 2-back tasks after confirming superior predictive performance over resting-state and volumetric data. High cross-task prediction accuracy as well as joint recruitment of canonical networks, such as the frontoparietal and default-mode networks, suggest the existence of a common executive function factor. To investigate the relationships among the three executive function components, we developed new measures to disentangle their shared and unique aspects. Our analysis confirmed that a shared executive function component can be predicted from functional connectivity patterns densely located around the frontoparietal, default-mode and dorsal attention networks. The Updating-specific component showed significant cross-prediction with the general executive function factor, suggesting a relatively stronger role than the other components. In contrast, the Shifting-specific and Inhibition-specific components exhibited lower cross-prediction performance, indicating more distinct and specialized roles. Given the limitation that individual behavioral measures do not purely reflect the intended cognitive constructs, our study demonstrates a novel approach to infer common and specific components of executive function.