Deep machine learning models including Convolutional Neural Networks (CNN) have been successful in the detection of Mild Cognitive Impairment (MCI) using medical images, questionnaires, and videos. This paper proposes a novel Multi-branch Classifier-Video Vision Transformer (MC-ViViT) model to distinguish MCI from those with normal cognition by analyzing facial features. The data comes from the I-CONECT, a behavioral intervention trial aimed at improving cognitive function by providing frequent video chats. MC-ViViT extracts spatiotemporal features of videos in one branch and augments representations by the MC module. The I-CONECT dataset is challenging as the dataset is imbalanced containing Hard-Easy and Positive-Negative samples, which impedes the performance of MC-ViViT. We propose a loss function for Hard-Easy and Positive-Negative Samples (HP Loss) by combining Focal loss and AD-CORRE loss to address the imbalanced problem. Our experimental results on the I-CONECT dataset show the great potential of MC-ViViT in predicting MCI with a high accuracy of 90.63\% accuracy on some of the interview videos.