Medical diagnostic robot systems have been paid more and more attention due to its objectivity and accuracy. The diagnosis of mild cognitive impairment (MCI) is considered an effective means to prevent Alzheimer's disease (AD). Doctors diagnose MCI based on various clinical examinations, which are expensive and the diagnosis results rely on the knowledge of doctors. Therefore, it is necessary to develop a robot diagnostic system to eliminate the influence of human factors and obtain a higher accuracy rate. In this paper, we propose a novel Group Feature Domain Adversarial Neural Network (GF- DANN) for amnestic MCI (aMCI) diagnosis, which involves two important modules. A Group Feature Extraction (GFE) module is proposed to reduce individual differences by learning group- level features through adversarial learning. A Dual Branch Domain Adaptation (DBDA) module is carefully designed to reduce the distribution difference between the source and target domain in a domain adaption way. On three types of data set, GF-DANN achieves the best accuracy compared with classic machine learning and deep learning methods. On the DMS data set, GF-DANN has obtained an accuracy rate of 89.47%, and the sensitivity and specificity are 90% and 89%. In addition, by comparing three EEG data collection paradigms, our results demonstrate that the DMS paradigm has the potential to build an aMCI diagnose robot system.