To meet the requirement of diverse geometric transformation and unstructured graph data for intelligent shape analysis method, this paper proposes a novel 3D graph recognition method based on geometric encoded feature learning, which effectively optimizes the feature extraction process from low-level geometry to high-level semantics, and improves the generalization and robustness of deep learning. Firstly, we adopt GMDS and KNN to build isometric embedding space and extract intrinsic geometric features. Secondly, in combination with the BoF method, the unified geometric encoded feature is generated, which effectively enhances the shape description ability of all kinds of graph data. Finally, an adaptive dynamic graph convolution network is established. Through dynamic spectral graph convolution and weighted feature refining, we implement efficient deep feature extraction and 3D graph recognition. A series of experimental results show that our proposed method achieves better performance in graph recognition and classification task. Moreover, whether the 3D graphs are rigid or non rigid, or incomplete and unconnected graph data, our method is significantly robust and efficient.