Attributed graph embedding, which learns vector representations,from graph topology and node features, is a challenging task for,graph analysis. Recently, methods based on graph convolutional,networks (GCNs) have made great progress on this task. However,,existing GCN-based methods have three major drawbacks. Firstly,,our experiments indicate that the entanglement of graph convolutional filters and weight matrices will harm both the performance,and robustness. Secondly, we show that graph convolutional filters,in these methods reveal to be special cases of generalized Laplacian,smoothing filters, but they do not preserve optimal low-pass characteristics. Finally, the training objectives of existing algorithms are,usually recovering the adjacency matrix or feature matrix, which,are not always consistent with real-world applications. To address,these issues, we propose Adaptive Graph Encoder (AGE), a novel,attributed graph embedding framework. AGE consists of two modules: (1) To better alleviate the high-frequency noises in the node,features, AGE first applies a carefully-designed Laplacian smoothing filter. (2) AGE employs an adaptive encoder that iteratively,strengthens the filtered features for better node embeddings. We,conduct experiments using four public benchmark datasets to validate AGE on node clustering and link prediction tasks. Experimental,results show that AGE consistently outperforms state-of-the-art,graph embedding methods considerably on these tasks.