In contrast to offline working fashions, two research paradigms are devised for online learning: (1) Online Meta Learning (OML) learns good priors over model parameters (or learning to learn) in a sequential setting where tasks are revealed one after another. Although it provides a sub-linear regret bound, such techniques completely ignore the importance of learning with fairness which is a significant hallmark of human intelligence. (2) Online Fairness-Aware Learning. This setting captures many classification problems for which fairness is a concern. But it aims to attain zero-shot generalization without any task-specific adaptation. This therefore limits the capability of a model to adapt onto newly arrived data. To overcome such issues and bridge the gap, in this paper for the first time we proposed a novel online meta-learning algorithm, namely FFML, which is under the setting of unfairness prevention. The key part of FFML is to learn good priors of an online fair classification model's primal and dual parameters that are associated with the model's accuracy and fairness, respectively. The problem is formulated in the form of a bi-level convex-concave optimization. Theoretic analysis provides sub-linear upper bounds for loss regret and for violation of cumulative fairness constraints. Our experiments demonstrate the versatility of FFML by applying it to classification on three real-world datasets and show substantial improvements over the best prior work on the tradeoff between fairness and classification accuracy