Phishing is a widespread scam activity on Ethereum, causing huge financial losses to victims. Most existing phishing scam detection methods abstract accounts on Ethereum as nodes and transactions as edges, then use manual statistics of static node features to obtain node embedding and finally identify phishing scams through classification models. However, these methods can not dynamically learn new Ethereum transactions. Since the phishing scams finished in a short time, a method that can detect phishing scams in real-time is needed. In this paper, we propose a streaming phishing scam detection method. To achieve streaming detection and capture the dynamic changes of Ethereum transactions, we first abstract transactions into edge features instead of node features, and then design a broadcast mechanism and a storage module, which integrate historical transaction information and neighbor transaction information to strengthen the node embedding. Finally, the node embedding can be learned from the storage module and the previous node embedding. Experimental results show that our method achieves decent performance on the Ethereum phishing scam detection task.