Graph neural networks are a useful tool to handle graph data. However, existing graph neural networks face the challenges of over-smoothing and over-squashing. In this work, we propose a Curvature-based topology-aware Dropout sampling technique which can be shortened as CurvDrop. We integrate the discrete ricci curvature into a powerful graph-based GNNs architecture to build a more expressive graph-based model. Also it expands the expressive to use more illuminating geometric descriptors to quantify the connections in graphs in modern models, and to extract desired structural information, such as inherent community structure in graphs with homogeneous information. As we expected, our methodology can tackle challenging problem with both over-smoothing and over-squashing simultaneously. On numerous datasets of various sizes, we tested our methodology, and the results were successful. Codes will be released upon acceptance.