In animal models, the incretin hormone GLP-1 affects Alzheimer’s disease (AD). We hypothesized that treatment with GLP-1 or an analog of GLP-1 would prevent accumulation of Aβ and raise, or prevent decline of, glucose metabolism (CMRglc) in AD. In this 26-week trial, we randomized 38 patients with AD to treatment with the GLP-1 analog liraglutide (n = 18), or placebo (n = 20). We measured Aβ load in brain with tracer [11C]PIB (PIB), CMRglc with [18F]FDG (FDG), and cognition with the WMS-IV scale (ClinicalTrials.gov NCT01469351). The PIB binding increased significantly in temporal lobe in placebo and treatment patients (both P = 0.04), and in occipital lobe in treatment patients (P = 0.04). Regional and global increases of PIB retention did not differ between the groups (P ≥ 0.38). In placebo treated patients CMRglc declined in all regions, significantly so by the following means in precuneus (P = 0.009, 3.2 μmol/hg/min, 95% CI: 5.45; 0.92), and in parietal (P = 0.04, 2.1 μmol/hg/min, 95% CI: 4.21; 0.081), temporal (P = 0.046, 1.54 μmol/hg/min, 95% CI: 3.05; 0.030), and occipital (P = 0.009, 2.10 μmol/hg/min, 95% CI: 3.61; 0.59) lobes, and in cerebellum (P = 0.04, 1.54 μmol/hg/min, 95% CI: 3.01; 0.064). In contrast, the GLP-1 analog treatment caused a numerical but insignificant increase of CMRglc after 6 months. Cognitive scores did not change. We conclude that the GLP-1 analog treatment prevented the decline of CMRglc that signifies cognitive impairment, synaptic dysfunction, and disease evolution. We draw no firm conclusions from the Aβ load or cognition measures, for which the study was underpowered.