Alzheimer's disease (AD) is a currently incurable neurodegenerative disease, with early detection representing a high research priority. AD is characterized by progressive cognitive decline accompanied by alterations in brain functional connectivity. Based on its data structure similar to the graph, graph neural networks (GNNs) have emerged as important methods for brain function analysis and disease prediction in recent years. However, most GNN methods are limited by information loss caused by traditional functional connectivity calculation as well as common noise issues in functional magnetic resonance imaging (fMRI) data. This paper proposes a graph generation based AD classification model using resting state fMRI to address this issue. The connectome generation network with large kernels for GNN (CGLK-GNN) based AD Analysis contains a graph generation block and a GNN prediction block. The graph generation block employs decoupled convolutional networks with large kernels to extract comprehensive temporal features while preserving sequential dependencies, contrasting with previous generative GNN approaches. This module constructs the connectome graph by encoding both edge-wise correlations and node-embedded temporal features, thereby utilizing the generated graph more effectively. The subsequent GNN prediction block adopts an efficient architecture to learn these enhanced representations and perform final AD stage classification. Through independent cohort validations, CGLK-GNN outperforms state-of-the-art GNN and rsfMRI-based AD classifiers in differentiating AD status. Furthermore, CGLK-GNN demonstrates high clinical value by learning clinically relevant connectome node and connectivity features from two independent datasets.