With the onset of the big data era, designing efficient and effective machine learning algorithms to analyze large-scale data is in dire need. In practice, data is typically generated by multiple parties and stored in a geographically distributed manner, which spurs the study of distributed machine learning. Traditional master-worker type of distributed machine learning algorithms assumes a trusted central server and focuses on the privacy issue in linear learning models, while privacy in nonlinear learning models and security issues are not well studied. To address these issues, in this paper, we explore the blockchain technique to propose a decentralized privacy-preserving and secure machine learning system, called LearningChain, by considering a general (linear or nonlinear) learning model and without a trusted central server. Specifically, we design a decentralized Stochastic Gradient Descent (SGD) algorithm to learn a general predictive model over the blockchain. In decentralized SGD, we develop differential privacy based schemes to protect each party’s data privacy, and propose an l-nearest aggregation algorithm to protect the system from potential Byzantine attacks. We also conduct theoretical analysis on the privacy and security of the proposed LearningChain. Finally, we implement LearningChain on Etheurum and demonstrate its efficiency and effectiveness through extensive experiments.