Early detection of Alzheimer's disease (AD) is important but difficult. Screening for AD using neuropsychological tests such as mini-mental state examination (MMSE) is time-consuming and burdensome for patients. Recently, several methods have been reported for detecting AD based on eye movements. However, analyzing eye movements requires considerable effort. Although machine learning from eye movement data is a strong candidate for labor-saving, it requires large datasets. In this study, we modify an existing pre-trained deep neural network model, gazeNet, for transfer learning. For evaluation, we exclusively used data from one participant and fine-tuned the model using data from all the remaining participants. We repeated this procedure separately for each of the 14 participants. The results of eye movement during the antisaccade task were not satisfactory for the discrimination of AD, and detailed analysis suggested that the data might potentially have a correlation with MMSE scores in the mild cognitive impairment range.