Hyperinsulinemia and type 2 diabetes (T2D) are important potential risk factors for cognitive decline and Alzheimer's disease (AD). Two thirds of the US adult population are at risk for hyperinsulinemia and T2D, and half of the population 85 years and older have AD. Peripheral hyperinsulinemia can impair the clearance of amyloid beta in the brain, the main culprit in AD. Thus, the investigators hypothesize that lowering peripheral insulin in overweight persons with amnestic mild cognitive impairment (AMCI), a transition state between normal cognition and AD, can decrease the risk of cognitive decline and progression to AD. The investigators propose to conduct a phase II double blinded placebo controlled randomized clinical trial of metformin, a safe and effective medication that prevents hyperinsulinemia and diabetes, to test this hypothesis among 80 overweight persons aged 55 to 90 years with AMCI. The main outcome of the study will be changes in performance in a memory test (total recall of the Selective Reminding Test) and the Score a test of general cognitive function used in clinical trials (the Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-Cog)). Another aim is to compare brain function in an area affected by Alzheimer's disease between the metformin and placebo group mean changes from beginning to end among 40 participants using a PET scan.
Inclusion criteria: * Age range: 55 years to 90 years. The main rationale for this inclusion criteria is to follow the standard set by the Alzheimer's Disease Cooperative Study (ADCS). * Memory complaint expressed by the participant and recognized by the informant. The memory complaint must represent a change from previous functioning based on information provided by both subject and informant. * Fluent in English or Spanish. * Mini-Mental State Examination (MMSE) equal or more than 20. * Subjects must fulfill criteria for amnestic mild cognitive impairment (MCI). Guidelines for the diagnosis of MCI: Subjects must score below a predetermined cut-off score on the logical memory II delayed paragraph recall sub-test of the Wechsler Memory Scale Revised (WMS-R) or the selective reminding test (SRT). * Global Clinical Dementia Rating (CDR) score must be 0.5 at screening. * Subjects without a known history of diabetes or diabetes that has never been treated with medications. If diabetes is diagnosed during screening or they have a history of diabetes not treated in the last 12 months they will be excluded if their Hemoglobin A1c (HbA1c) is \> 6.5. In addition, a diagnosis of diabetes can be made if the HbA1c is 6.5% or more. * Overweight or obese by National Heart, Lung, and Blood Institute (NHLBI) criteria (Body Mass Index (BMI) of more or equal of 25 kg/ m2). * No contraindications to metformin treatment. * Hachinski score less or equal to 4. * Hamilton score less or equal to 12 on the 17 item scale. * General cognition and functional performance such that a diagnosis of dementia cannot be made at the time of screening based on DSM-IV criteria. * Vision and hearing must be sufficient for compliance with testing procedures. Exclusion criteria: * Individuals with dementia * MMSE \< 20 * Subjects with neurologic diseases associated to neurologic deficits. * Subjects with current psychiatric diagnoses such as depression, bipolar disorder or schizophrenia. * Subjects with uncontrolled hypertension (systolic blood pressure more than 160 mmHg or diastolic blood pressure more than 95 mmHg. * Subjects with a history of active cancer or cancer within last five years, with the exception of squamous or basal cell carcinoma of the skin. * Subjects who for any reason may not complete the study as judged by the study physician. * Subjects with a known history of diabetes treated with medications. * Subjects with a new or old diagnosis of diabetes, never treated, with a HbA1c of more than 6.5 . * Contraindications to metformin: Contraindications to metformin use include a creatinine of \> 1.5, liver disease by history or by elevated transaminases, congestive heart failure, and alcohol abuse. * Use of cholinesterase inhibitors. Exclusion criteria for brain imaging study: * Presence of diabetes, even if the HbA1c is less or equal to 6.5. * Inability to lie down for any reason. * Presence of any metallic implant. * Claustrophobia. * Any contraindication to magnetic resonance imaging (MRI) or fluorodeoxyglucose (FDG) positron emission tomography (PET).