Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, driving advancements across diverse fields such as traffic networks, recommendation systems, and molecular biology. Despite their impressive performance, GNNs still encounter several challenges, including limited robustness, over-smoothing, and susceptibility to overfitting. To deal with these issues, we design a novel dropout strategy called ANDS which consists of two steps: It conducts two iteration aggregation (i.e. GNN layer) and then propagates the information through several branches using different perturbed adjacency matrixes. To justify the effectiveness of our proposal, we perform several experiments on two graph citation datasets. Numerical results prove the efficiency of the proposed scheme in enhancing robustness and alleviating the over-smoothing issue.