Alzheimer’s disease (AD) is one of the most common progressive neurodegenerative diseases, and the number of AD patients has increased year after year with the global aging trend. The onset of AD has a long preclinical stage. If doctors can make an initial diagnosis in the mild cognitive impairment (MCI) stage, it is possible to identify and screen those at a high-risk of developing full-blown AD, and thus the number of new AD patients can be reduced. However, there are problems with the medical datasets including AD data, such as insufficient number of samples and different data distributions. Transfer learning, which can effectively solve the problem of distribution discrepancy between training and test data and an insufficient number of target samples, has attracted increasing attention over recent years. In this paper, we propose a multi-source ensemble transfer learning (METL) approach by introducing ensemble learning and our tri-transfer model that uses Tri-Training, which ensures the transferability of source data by the tri-transfer model and high performance through ensemble learning. The experimental results on the benchmark and AD datasets demonstrate that our proposed approach has effective transferability, robustness, and feasibility, and is superior to existing algorithms. Based on METL, we propose an auxiliary diagnosis system for the initial diagnosis of AD, which helps doctors identify patients in the MCI stage as quickly as possible and with high accuracy so that measures can be taken to prevent or delay the occurrence of AD.