Blockchain-based supply chain (BSC) systems have tremendously been developed recently and can play an important role in our society in the future. In this study, we develop an anomaly detection model for BSC systems. Our proposed model can detect cyber-attacks at various levels, including the network layer, consensus layer, and beyond, by analyzing only the traffic data at the network layer. To do this, we first build a BSC system at our laboratory to perform experiments and collect datasets. We then propose a novel semi-supervised DAE-MLP (Deep AutoEncoder-Multilayer Perceptron) that combines the advantages of supervised and unsupervised learning to detect anomalies in BSC systems. The experimental results demonstrate the effectiveness of our model for anomaly detection within BSCs, achieving a detection accuracy of 96.5%. Moreover, DAE-MLP can effectively detect new attacks by improving the F1-score up to 33.1% after updating the MLP component.