Abnormal glucose metabolism and hemodynamic changes in the brain are closely related to cognitive function, providing complementary information from distinct biochemical and physiological processes. However, it remains unclear how to effectively integrate these two modalities across distinct brain regions. In this study, we developed a connectome-based sparse coupling method for hybrid PET/MRI imaging, which could effectively extract imaging markers of Alzheimer's disease (AD) in the early stage. The FDG-PET and resting-state fMRI data of 56 healthy controls (HC), 54 subjective cognitive decline (SCD), and 27 cognitive impairment (CI) participants due to AD were obtained from SILCODE project (NCT03370744). For each participant, the metabolic connectome (MC) was constructed by Kullback-Leibler divergence similarity estimation, and the functional connectome (FC) was constructed by Pearson correlation. Subsequently, we measured the coupling strength between MC and FC at various sparse levels, assessed its stability, and explored the abnormal coupling strength along the AD continuum. Results showed that the sparse MC-FC coupling index was stable in each brain network and consistent across subjects. It was more normally distributed than other traditional indexes and captured more SCD-related brain areas, especially in the limbic and default mode networks. Compared to other traditional indices, this index demonstrated best classification performance. The AUC values reached 0.748 (SCD/HC) and 0.992 (CI/HC). Notably, we found a significant correlation between abnormal coupling strength and neuropsychological scales (p < .05). This study provides a clinically relevant tool for hybrid PET/MRI imaging, allowing for exploring imaging markers in early stage of AD and better understanding the pathophysiology along the AD continuum.© 2023 The Authors. Human Brain Mapping published by Wiley Periodicals LLC.