Background: People with type 2 diabetes are at risk of cognitive impairment and brain atrophy. We aimed to compare the effects on cognitive function and brain volume of intensive versus standard glycaemic control. Methods: The Memory in Diabetes (MIND) study was done in 52 clinical sites in North America as part of Action to Control Cardiovascular Risk in Diabetes (ACCORD), a double two-by-two factorial parallel group randomised trial. Participants (aged 55-80 years) with type 2 diabetes, high glycated haemoglobin A 1c (HbA 1c) concentrations (>7·5%; >58 mmol/mol), and a high risk of cardiovascular events were randomly assigned to receive intensive glycaemic control targeting HbA 1c to less than 6·0% (42 mmol/mol) or a standard strategy targeting HbA 1c to 7·0-7·9% (53-63 mmol/mol). Randomisation was via a centralised web-based system and treatment allocation was not masked from clinic staff or participants. We assessed our cognitive primary outcome, the Digit Symbol Substitution Test (DSST) score, at baseline and at 20 and 40 months. We assessed total brain volume (TBV), our primary brain structure outcome, with MRI at baseline and 40 months in a subset of participants. We included all participants with follow-up data in our primary analyses. In February, 2008, raised mortality risk led to the end of the intensive treatment and transition of those participants to standard treatment. We tested our cognitive function hypotheses with a mixed-effects model that incorporated information from both the 20 and 40 month outcome measures. We tested our MRI hypotheses with an ANCOVA model that included intracranial volume and factors used to stratify randomisation. This study is registered with ClinicalTrials.gov, number NCT00182910. Findings: We consecutively enrolled 2977 patients (mean age 62·5 years; SD 5·8) who had been randomly assigned to treatment groups in the ACCORD study. Our primary cognitive analysis was of patients with a 20-month or 40-month DSST score: 1378 assigned to receive intensive treatment and 1416 assigned to receive standard treatment. Of the 614 patients with a baseline MRI, we included 230 assigned to receive intensive treatment and 273 assigned to receive standard treatment in our primary MRI analysis at 40 months. There was no significant treatment difference in mean 40-month DSST score (difference in mean 0·32, 95% CI -0·28 to 0·91; p=0·2997). The intensive-treatment group had a greater mean TBV than the standard-treatment group (4·62, 2·0 to 7·3; p=0·0007). Interpretation: Although significant differences in TBV favoured the intensive treatment, cognitive outcomes were not different. Combined with the non-significant effects on other ACCORD outcomes, and increased mortality in participants in the intensive treatment group, our findings do not support the use of intensive therapy to reduce the adverse effects of diabetes on the brain in patients with similar characteristics to those of our participants. Funding: US National Institute on Aging and US National Heart, Lung, and Blood Institute. © 2011 Elsevier Ltd.