While convolutional neural network (CNN) has been demonstrating powerful ability to learn hierarchical spatial features from medical images, it is still difficult to apply it directly to resting-state functional MRI (rs-fMRI) and the derived brain functional networks (BFNs). We propose a novel CNN framework to simultaneously learn embedded features from BFNs for brain disease diagnosis. Since BFNs can be built by considering both static and dynamic functional connectivity (FC), we first decompose rs-fMRI into multiple static BFNs with modified independent component analysis. Then, the voxel-wise variability in dynamic FC is used to quantify BFN dynamics. A set of paired 3D images representing static/dynamic BFNs can be fed into 3D CNNs, from which we can hierarchically and simultaneously learn static/dynamic BFN features. As a result, the dynamic BFN features can complement static BFN features and, at the meantime, different BFNs can help each other toward a joint and better classification. We validate our method with a publicly accessible, large cohort of rs-fMRI dataset in early-stage mild cognitive impairment (eMCI) diagnosis, which is one of the most challenging problems to the clinicians. By comparing with a conventional method, our method shows significant diagnostic performance improvement by almost 10%. This result demonstrates the effectiveness of deep learning in preclinical Alzheimer's disease diagnosis, based on the complex and high-dimensional voxel-wise spatiotemporal patterns of the resting-state brain functional connectomics. The framework provides a new but intuitive way to fully exploit deeply embedded diagnostic features from rs-fMRI for a better-individualized diagnosis of various neurological diseases.