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 (CMR_glc) 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), CMR_glc 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 CMR_glc 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 CMR_glc after 6 months. Cognitive scores did not change. We conclude that the GLP-1 analog treatment prevented the decline of CMR_glc 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.