This paper proposed a new online continual learning approach called OCMM based on \textit{mutual information} (MI) \textit{maximization}. It achieves two objectives that are critical in dealing with catastrophic forgetting (CF). {\color{black}(1) It reduces feature bias caused by cross entropy (CE) as CE learns only discriminative features for each task, but these features may not be discriminative for another task. To learn a new task well, the network parameters learned before have to be modified, which causes CF.} The new approach encourages the learning of each task to make use of the full features of the task training data. (2) It encourages preservation of the previously learned knowledge when training a new batch of incrementally arriving data. Empirical evaluation shows that OCMM substantially outperforms the latest online CL baselines. For example, for CIFAR10, OCMM improves the accuracy of the best baseline by 13.1\% from 64.1\% (baseline) to 77.2\% (OCMM).The code is publicly available at https://github.com/gydpku/OCM.