We consider a collaborative learning scenario in which multiple data-owners wish to jointly train a logistic regression model, while keeping their individual datasets private from the other parties. We propose COPML, a fully-decentralized training framework that achieves scalability and privacy-protection simultaneously. The key idea of COPML is to securely encode the individual datasets to distribute the computation load effectively across many parties and to perform the training computations as well as the model updates in a distributed manner on the securely encoded data. We provide the privacy analysis of COPML and prove its convergence. Furthermore, we experimentally demonstrate that COPML can achieve significant speedup in training over the benchmark protocols. Our protocol provides strong statistical privacy guarantees against colluding parties (adversaries) with unbounded computational power, while achieving up to $16times$ speedup in the training time against the benchmark protocols.