Although alternations of brain functional networks (BFNs) derived from resting-state functional magnetic resonance imaging (rs-fMRI) have been considered as promising biomarkers for early Alzheimer’s disease (AD) diagnosis, it is still challenging to perform individualized diagnosis, especially at the very early stage of preclinical stage of AD, i.e., early mild cognitive impairment (eMCI). Recently, convolutional neural networks (CNNs) show powerful ability in computer vision and image analysis applications, but there is still a gap for directly applying CNNs to rs-fMRI-based disease diagnosis. In this paper, we propose a novel multiple-BFN-based 3D CNN framework that can automatically and deeply learn complex, high-level, hierarchical diagnostic features from various independent component analysis-derived BFNs. More importantly, the embedded features of different BFNs could comprehensively support each other towards a more accurate eMCI diagnosis in a unified model. The performance of the proposed method is validated by a large-sample, multisite, rigorously controlled publicly accessible dataset. The proposed framework can also be conveniently and straightforwardly applied to individualized diagnosis of various neurological and psychiatric diseases.