Glucose metabolism reduction and brain volume losses are widely reported in Alzheimer’s disease (AD). Considering that neuroimaging changes in the hippocampus and default mode network (DMN) are promising important candidate biomarkers and have been included in the research criteria for the diagnosis of AD, it is hypothesized that atrophy and metabolic changes of the abovementioned regions could be evaluated concurrently to fully explore the neural mechanisms underlying cognitive impairment in AD. Twenty-three AD patients and Twenty-four age-, sex- and education level-matched normal controls underwent a clinical interview, a detailed neuropsychological assessment and a simultaneous 18F-fluoro-2-deoxy-D-glucose positron emission tomography (18F-FDG PET)/high-resolution T1-weighted magnetic resonance imaging (MRI) scan on a hybrid GE SIGNA PET/MR scanner. Brain volume and glucose metabolism were examined in patients and controls to reveal group differences. Multiple linear regression models were employed to explore the relationship between multiple imaging features and cognitive performance in AD. The AD group had significantly reduced volume in the hippocampus and DMN regions (P < 0.001) relative to that of normal controls determined by using ROI analysis. Compared to normal controls, significantly decreased metabolism in the DMN (P < 0.001) was also found in AD patients, which still survived after controlling for gray matter atrophy (P < 0.001). These findings from ROI analysis were further confirmed by whole-brain confirmatory analysis (P < 0.001, FWE-corrected). Finally, multiple linear regression results showed that impairment of multiple cognitive tasks was significantly correlated with the combination of DMN hypometabolism and atrophy in the hippocampus and DMN regions. This study demonstrated that combining functional and structural features can better explain the cognitive decline of AD patients than unimodal FDG or brain volume changes alone. These findings may have important implications for understanding the neural mechanisms of cognitive decline in AD.