Mild cognitive impairment (MCI) is a preclinical stage of Alzheimer's disease (AD), and early diagnosis and intervention may delay its deterioration. However, the electroencephalogram (EEG) differences between patients with amnestic mild cognitive impairment (aMCI) and healthy controls (HC) subjects are not as significant compared to those with AD. This study addresses this situation by proposing a computer-aided diagnostic method that also aims to improve model performance and assess the sensitive areas of the subject's brain. The EEG data of 46 subjects (20HC/26aMCI) were enhanced with windowed moving segmentation and transformed from 1D temporal data to 2D spectral entropy images to measure the efficient information in the time-frequency domain from the point of view of information entropy; A novel convolution module is devised, which considerably reduces the number of model learning parameters and saves computing resources on the premise of ensuring diagnostic performance; One more thing, the cognitive diagnostic contribution of the corresponding channels in each brain region was measured by the weight coefficient of the input and convolution unit. Our results showed that when the segmental window overlap rate was increased from 0 to 75%, the corresponding generalization accuracy increased from 91.673 +/- 0.9578% to 94.642 +/- 0.4035%; Approximately 35% reduction in model learnable parameters by optimizing the network structure while maintaining accuracy; The top four channels were FP1, F7, T5, and F4, corresponding to the frontal and temporal lobes, in descending order of the mean value of the weight coefficients. This paper proposes a novel method based on spectral entropy image and convolutional neural network (CNN), which provides a new perspective for the identifying of aMCI based on EEG.