Cognitive control is a critical higher mental function, which is subject to considerable individual variation and is impaired in a range of mental health disorders. We describe here the initial release of Dual Mechanisms of Cognitive Control (DMCC) project data, the DMCC55B dataset, with 55 healthy unrelated young adult participants. Each participant performed four well-established cognitive control tasks (Stroop, AX-CPT, Cued Task-Switching, and Sternberg Working Memory) while undergoing moderately high-resolution functional MRI scanning. The dataset includes a range of state and trait self-report questionnaires, as well as behavioural tasks assessing individual differences in cognitive ability. The DMCC project is on-going and features additional components (e.g., related participants, manipulations of cognitive control mode, resting state fMRI, longitudinal testing) that will be publicly released following study completion. This DMCC55B subset is released early with the aim of encouraging wider use and greater benefit to the scientific community. The DMCC55B dataset is suitable for benchmarking and methods exploration, as well as analyses of task performance and individual differences.