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Background: Structural magnetic resonance imaging (sMRI) can provide morphological information about the structure and function of the brain in the same scanning process. It has been widely used in the diagnosis of Alzheimer's disease (AD) and mild cognitive impairment (MCI). Purpose: To capture the anatomical changes in the brain caused by AD/MCI, deep learning‐based MRI image analysis methods have been proposed in recent years. However, it is observed that the performance of most existing methods is limited as they only construct a single type of deep network and ignore the significance of other clinical information. Methods: To make up for these defects, an ensemble framework that incorporates three types of dedicatedly‐designed convolutional neural networks (CNNs) and a multilayer perceptron (MLP) network is proposed, where three CNNs with entropy‐based multi‐instance learning pooling layers have more reliable feature selection abilities. The dedicatedly‐designed base classifiers can make use of the heterogeneous data, and empower the framework with enhanced diversity and robustness. In particular, to consider the interactions among the base classifiers, a novel multi‐head self‐attention voting scheme is designed. Moreover, considering the chance that MCI can be transformed to AD, the proposed framework is designed to diagnose AD and predict MCI conversion simultaneously, with the aid of the transfer learning technique. Results: For performance evaluation and comparison, extensive experiments are conducted on the public dataset of the Alzheimer's Disease Neuroimaging Initiative (ADNI). The results show that the proposed ensemble framework provides superior performance under most of the evaluation metrics. Especially, the proposed framework achieves state‐of‐the‐art diagnostic accuracy (98.61% for the AD diagnosis task, and 84.49% for the MCI conversion prediction task). Conclusions: These promising results demonstrate the proposed ensemble framework can accurately diagnose AD patients and predict the conversion of MCI patients, which has the potential of clinical practice for diagnosing AD and MCI. [ABSTRACT FROM AUTHOR]