Nearly half of all mild brain injury sufferers experience long-term cognitive impairment, so an important goal in rehabilitation is to address their multiple cognitive deficits to help them return to prior levels of functioning. Cognitive training, or the use of repeated mental exercises to enhance cognition, is one remediation method for brain injury. The primary purpose of this hypothesis-generating pilot study was to explore the statistical and clinical significance of cognitive changes and transfer of training to real-life functioning following 60 h of Brain Booster, a clinician-delivered cognitive training program, for six patients with mild traumatic brain injury (TBI) or non-traumatic acquired brain injury (ABI). The secondary purpose was to explore changes in functional connectivity and neural correlates of cognitive test gains following the training. We used a multiple case study design to document significant changes in cognitive test scores, overall IQ score, and symptom ratings; and we used magnetic resonance imaging (MRI) to explore trends in functional network connectivity and neural correlates of cognitive change. All cognitive test scores showed improvement with statistically significant changes on five of the seven measures (long-term memory, processing speed, reasoning, auditory processing, and overall IQ score). The mean change in IQ score was 20 points, from a mean of 108 to a mean of 128. Five themes emerged from the qualitative data analysis including improvements in cognition, mood, social identity, performance, and Instrumental Activities of Daily Living (IADLs). With MRI, we documented significant region-to-region changes in connectivity following cognitive training including those involving the cerebellum and cerebellar networks. We also found significant correlations between changes in IQ score and change in white matter integrity of bilateral corticospinal tracts (CST) and the left uncinate fasciculus. This study adds to the growing body of literature examining the effects of cognitive training for mild TBI and ABI, and to the collection of research on the benefits of cognitive training in general. Clinical Trial Registration: www.ClinicalTrials.gov, identifier NCT02918994.