We propose a new STAcked and Reconstructed Graph Convolutional Networks (STAR-GCN) architecture to learn node representations for boosting the performance in recommender systems, especially in the cold start scenario. STAR-GCN employs a stack of GCN encoder-decoders combined with intermediate supervision to improve the final prediction performance. Unlike the graph convolutional matrix completion model with one-hot encoding node inputs, our STAR-GCN learns low-dimensional user and item latent factors as the input to restrain the model space complexity. Moreover, our STAR-GCN can produce node embeddings for new nodes by reconstructing masked input node embeddings, which essentially tackles the cold start problem. Furthermore, we discover a label leakage issue when training GCN-based models for link prediction tasks and propose a training strategy to avoid the issue. Empirical results on multiple rating prediction benchmarks demonstrate our model achieves state-of-the-art performance in four out of five real-world datasets and significant improvements in predicting ratings in the cold start scenario. The code implementation is available in https://github.com/jennyzhang0215/STAR-GCN.