With the rapid growth of blockchain, an increasing number of users have been attracted and many implementations have been refreshed in different fields. Especially in the cryptocurrency investment field, blockchain technology has shown vigorous vitality. However, along with the rise of online business, numerous fraudulent activities, e.g., money laundering, bribery, phishing, and others, emerge as the main threat to trading security. Due to the openness of Ethereum, researchers can easily access Ethereum transaction records and smart contracts, which brings unprecedented opportunities for Ethereum scams detection and analysis. This paper mainly focuses on the Ponzi scheme, a typical fraud, which has caused large property damage to the users in Ethereum. By verifying Ponzi contracts to maintain Ethereum's sustainable development, we model Ponzi scheme identification and detection as a node classification task. In this paper, we first collect target contracts' transactions to establish transaction networks and propose a detecting model based on graph convolutional network (GCN) to precisely distinguishPonzi contracts. Experiments on different real-world Ethereum datasets demonstrate that our proposed model has promising results compared with general machine learning methods to detect Ponzi schemes.