This article focuses on the online distributed optimization with privacy protection in time-varying unbalanced networks. We consider the case where there exist potential passive attackers in the network, having access to all communication channels. The attackers attempt to deduce the privacy of participating nodes. In this case, the differential privacy approach is leveraged to enable privacy protection. Based on this privacy-preserving approach and the stochastic subgradient method, a novel differentially private distributed online stochastic subgradient descent (DP-DOSSD) algorithm is devised for addressing the considered problem. Unlike the existing algorithms that require the weight matrices to be doubly stochastic, our algorithm only depends on two different weight matrices that are column-stochastic and row-stochastic, respectively. Moreover, a stochastic subgradient rescaling technique is adopted to tackle the unbalancedness of time-varying directed networks. It proves that our algorithm not only guarantees ϵ-differential privacy but also establishes an expected regret of orderO(√T) in convex settings, where ϵ andTare the privacy level and the time horizon, respectively. The established result matches the optimal regret bound derived by state-of-the-art algorithms. The fundamental tradeoff between convergence performance and privacy level is also studied. Finally, simulation results for the sensor network-based online distributed estimation problem and the distributed online ridge regression problem are provided to confirm the effectiveness of our approach.