Aiming at the problem of learning streaming data collected by a decentralized network in an online manner, a decentralized online learning algorithm — Decentralized Online alternating direction method of Multipliers (DOM) was proposed based on the Alternating Direction Method of Multipliers (ADMM). Firstly, observing that decentralized online learning required each node to update its local iterate based on new local data while keeping the estimation of all the nodes converged to a consensual iterate, a mathematical model was developed and solved by DOM. Secondly, a Regret bound of decentralized online learning was defined to evaluate performance of online estimation. DOM was proved to be convergent when the instantaneous local cost functions were convex, and the convergence rate was given. Finally, the results of numerical experiments show that, compared with existing algorithms such as Distributed Online Gradient Descent (DOGD) and Distributed Autonomous Online Learning (DAOL), the proposed algorithm DOM has the fastest convergence rate.