Quantum Error Correction (QEC) is vital for fault tolerant quantum computation and requires fast and high-performance decoder. In recent years, a large number of methods for machine learning based decoders have been proposed. However, none of them explicitly utilize the local connection of the error correction codes, such as color codes and rotated surface code, or the correlation of the X and Z syndrome qubits in the case of depolarizing noise models. In this presentation, we address these problems by deploying Graph Convolutional Network (GCN) and show numerical results obtained from it.