BACKGROUND: Home-based computerised cognitive training (CCT) is ineffective at enhancing global cognition, a key marker of cognitive ageing. OBJECTIVES: To test the effectiveness of supervised, group-based, multidomain CCT on global cognition in older adults and to characterise the dose-response relationship during and after training. DESIGN: A randomised, double-blind, longitudinal, active-controlled trial. SETTING: Community-based training centre in Sydney, Australia Participants: Eighty nondemented community-dwelling older adults (mean age = 72.1, 68.8% females) with multiple dementia risk factors but no major neuropsychiatric or sensory disorder. Of the 80 participants admitted to the study, 65 completed post-training assessment and 55 were followed up one year after training cessation. INTERVENTIONS: Thirty-six group-based sessions over three months of either CCT targeting memory, speed, attention, language and reasoning tasks, or active control training comprising audiovisual educational exercises. MEASUREMENTS: Primary outcome was change from baseline in global cognition as defined by a composite score of memory, speed and executive function. Secondary outcome was 15-month change in Bayer Activities of Daily Living from baseline to one year post-training. RESULTS: Intention-to-treat analyses revealed significant effects on global cognition in the cognitive training group compared to active control after three weeks of training (ES = 0.33, P=.039) that increased after 3 months of training (ES = 0.49, P=.003) and persisted three months after training cessation (ES = 0.30, P=0.023). Significant and durable improvements were also noted in memory and processing speed. Dose-response characteristics differed among cognitive domains. Training effects waned gradually but residual gains were noted twelve months post-training. No significant effects on activities of daily living were noted and there were no adverse effects. CONCLUSIONS: In older adults with multiple dementia risk factors, group-based CCT is a safe and effective intervention for enhancing overall cognition, memory and processing speed. Dose-response relationships vary for each cognitive domain, vital information for clinical and community implementation and further trial design.