Whether brain training programmes are effective and have transferable benefits to wider cognitive abilities is controversial, especially in older adult populations. We assessed, in a randomised controlled intervention study, whether a commercially available brain training programme can induce cognitive improvements in a sample of healthy older adults (N = 103). Participants completed a three-month intervention of either an adaptive computerised cognitive training programme (through a brain training app) or active control. Cognition was measured through a comprehensive battery of tasks pre- and post-intervention to assess working memory, processing speed, attention, and language functioning. Participants in the intervention group significantly improved on all tasks that were trained specifically within the brain training programme (i.e. practice effects). However, for the cognitive tasks assessed pre- and post-intervention there was no evidence of any of these practice effects transferring to improvements in cognitive outcome measures compared to the active control group (i.e. transfer effects). Our results indicate that the benefits of brain training programmes appear to be limited to practice effects of trained tasks, while no evidence is found for transfer effects to other, related or unrelated, untrained cognitive tasks.