Early diagnosis and intervention of mild cognitive impairment (MCI) and its early stage (i.e., subjective cognitive decline (SCD)) is able to delay or reverse the disease progression. However, discrimination between SCD, MCI and healthy subjects accurately remains challenging. This paper proposes an auto-weighted centralised multi-task (AWCMT) learning framework for differential diagnosis of SCD and MCI. AWCMT is based on structural and functional connectivity information inferred from magnetic resonance imaging (MRI). To be specific, we devise a novel multi-task learning algorithm to combine neuroimaging functional and structural connective information. We construct a functional brain network through a sparse and low-rank machine learning method, and also a structural brain network via fibre bundle tracking. Those two networks are constructed separately and independently. Multi-task learning is then used to identify features integration of functional and structural connectivity. Hence, we can learn each task's significance automatically in a balanced way. By combining the functional and structural information, the most informative features of SCD and MCI are obtained for diagnosis. The extensive experiments on the public and self-collected datasets demonstrate that the proposed algorithm obtains better performance in classifying SCD, MCI and healthy people than traditional algorithms. The newly proposed method has good interpretability as it is able to discover the most disease-related brain regions and their connectivity. The results agree well with current clinical findings and provide new insights into early AD detection based on the multi-modal neuroimaging technique.Copyright © 2021 Elsevier B.V. All rights reserved.