Few studies to date have investigated the background network in the cognitive state relying on executive function in mild cognitive impairment (MCI) patients. Using the index of degree of centrality (DC), we explored distant synchronization of background network in MCI during a hybrid delayed-match-to-sample task (DMST), which mainly relies on the working memory component of executive function. We observed significant interactions between group and cognitive state in the bilateral posterior cingulate cortex (PCC) and the ventral subregion of precuneus. For normal control (NC) group, the long distance functional connectivity (FC) of the PCC/precuneus with the other regions of the brain was higher in rest state than that working memory state. For MCI patients, however, this pattern altered. There was no significant difference between rest and working memory state. The similar pattern was observed in the other cluster located in the right angular gyrus. To examine whether abnormal DC in PCC/precuneus and angular gyrus partially resulted from the deficit of FC between these regions and the other parts in the whole brain, we conducted a seed-based correlation analysis with these regions as seeds. The results indicated that the FC between bilateral PCC/precuneus and the right inferior parietal lobule (IPL) increased from rest to working memory state for NC participants. For MCI patients, however, there was no significant change between rest and working memory state. The similar pattern was observed for the FC between right angular gyrus and right anterior insula. However, there was no difference between MCI and NC groups in global efficiency and modularity. It may indicate a lack of efficient reorganization from rest state to a working memory state in the brain network of MCI patients. The present study demonstrates the altered distant synchronization of background network in MCI during a task relying on executive function. The results provide a new perspective regarding the neural mechanisms of executive function deficits in MCI patients, and extend our understanding of brain patterns in task-evoked cognitive states.