Diabetes is a significant public health issue as it increases the risk for dementia and Alzheimer’s disease (AD). In this study, we aim to investigate whether weighted-permutation entropy (WPE) and permutation entropy (PE) of resting-state EEG (rsEEG) could be applied as potential objective biomarkers to distinguish type 2 diabetes patients with amnestic mild cognitive impairment (aMCI) from those with normal cognitive function. rsEEG series were acquired from 28 patients with type 2 diabetes (16 aMCI patients and 12 controls), and neuropsychological assessments were performed. The rsEEG signals were analysed using WPE and PE methods. The correlations between the PE or WPE of the rsEEG and the neuropsychological assessments were analysed as well. The WPE in the right temporal (RT) region of the aMCI diabetics was lower than the controls, and the WPE was significantly positively correlated to the scores of the Auditory Verbal Learning Test (AVLT) (AVLT-Immediate recall, AVLT-Delayed recall, AVLT-Delayed recognition) and the Wechsler Adult Intelligence Scale Digit Span Test (WAIS-DST). These findings were not obtained with PE. We concluded that the WPE of rsEEG recordings could distinguish aMCI diabetics from normal cognitive function diabetic controls among the current sample of diabetic patients. Thus, the WPE could be a potential index for assisting diagnosis of aMCI in type 2 diabetes.