Graph Neural Networks (GNNs) have achieved state-of-the-art performance in many graph data analysis tasks. However, they still suffer from two limitations for graph represen-tation learning. First, they exploit non-smoothing node fea-tures which may result in suboptimal embedding and degen-erated performance for graph classification. Second, they on-ly exploit neighbor information but ignore global topologicalknowledge. Aiming to overcome these limitations simultane-ously, in this paper, we propose a novel, flexible, and end-to-end framework, Graph Smoothing Splines Neural Networks(GSSNN), for graph classification. By exploiting the smooth-ing splines, which are widely used to learn smoothing fit-ting function in regression, we develop an effective featuresmoothing and enhancement module Scaled Smoothing S-plines (S3) to learn graph embedding. To integrate globaltopological information, we design a novel scoring module,which exploits closeness, degree, as well as self-attention val-ues, to select important node features as knots for smoothingsplines. These knots can be potentially used for interpretingclassification results. In extensive experiments on biologicaland social datasets, we demonstrate that our model achievesstate-of-the-arts and GSSNN is superior in learning more ro-bust graph representations. Furthermore, we show that S3module is easily plugged into existing GNNs to improve theirperformance.