As data volume and complexity of the machine learning model increase, designing a secure and effective distributed machine learning (DML) algorithm is in direct need. Most traditional master-worker type of DML algorithms assume a trusted central server and study security issues on workers. Several researchers bridged DML and blockchain to defend against malicious central servers. However, some critical challenges remain, such as not being able to identify Byzantine nodes, not being robust to Byzantine attacks, requiring large communication overhead. To address these issues, in this paper, we propose a permissioned blockchain framework for secure DML. called Secure Learning Chain (SLC). Specifically, we design an Identifiable Practical Byzantine Fault Tolerance (IPBFT) consensus algorithm to defend against malicious central servers. This algorithm can also identify malicious central servers and reduce communication complexity. In addition, we propose a Mixed Ace-based multi-Krum Aggregation (MAKA) algorithm to prevent Byzantine attacks from malicious workers. Finally, our experiment results demonstrate our proposed model's efficiency and effectiveness.