Alzheimer's Disease (AD) is a currently incurable neurodegeneartive disease. Accurately detecting AD, especially in the early stage, represents a high research priority. AD is characterized by progressive cognitive impairments that are related to alterations in brain functional connectivity (FC). Based on this association, many studies have been published over the decades using FC and machine learning to differentiate AD from healthy aging. The most recent development in this detection method highlights the use of graph neural network (GNN) as the brain functionality analysis. In this paper, we proposed a stack of spatio-temporal feature extraction and graph generation based AD classification model using resting state fMRI. The proposed multi-level generated connectome (MLC) based graph convolutional network (GCN) (MLC-GCN) contains a multi-graph generation block and a GCN prediction block. The multi-graph generation block consists of a hierarchy of spatio-temporal feature extraction layers for extracting spatio-temporal rsfMRI features at different depths and building the corresponding connectomes. The GCN prediction block takes the learned multi-level connectomes to build and optimize GCNs at each level and concatenates the learned graphical features as the final predicting features for AD classification. Through independent cohort validations, MLC-GCN shows better performance for differentiating MCI, AD, and normal aging than state-of-art GCN and rsfMRI based AD classifiers. The proposed MLC-GCN also showed high explainability in terms of learning clinically reasonable connectome node and connectivity features from two independent datasets. While we only tested MLC-GCN on AD, the basic rsfMRI-based multi-level learned GCN based outcome prediction strategy is valid for other diseases or clinical outcomes.