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The decoupled Graph Convolutional Network (GCN), a recent development of GCN that decouples the neighborhood aggregation and feature transformation in each convolutional layer, has shown promising performance for graph representation learning. Existing decoupled GCNs first utilize a simple neural network (e.g., MLP) to learn the hidden features of the nodes, then propagate the learned features on the graph with fixed steps to aggregate the information of multi-hop neighborhoods. Despite effectiveness, the aggregation operation, which requires the whole adjacency matrix as the input, is involved in the model training, causing high training cost that hinders its potential on larger graphs. On the other hand, due to the independence of node attributes as the input, the neural networks used in decoupled GCNs are very simple, and advanced techniques cannot be applied to the modeling. To this end, we further liberate the aggregation operation from the decoupled GCN and propose a new paradigm of GCN, termed Neighborhood Convolutional Network (NCN), that utilizes the neighborhood aggregation result as the input, followed by a special convolutional neural network tailored for extracting expressive node representations from the aggregation input. In this way, the model could inherit the merit of decoupled GCN for aggregating neighborhood information, at the same time, develop much more powerful feature learning modules. A training strategy called mask training is incorporated to further boost the model performance. Extensive results demonstrate the effectiveness of our model for the node classification task on diverse homophilic graphs and heterophilic graphs.