We study online batch recommendation in which one item is recommended to each user and the reward is returned from the user at each round. Users are assumed to be partitioned into groups and the task of the recommender system is to decide the probability distribution of the items for each group of users to send the next round of recommendations. The objective of the recommender system is to maximize the cumulative reward summed up for all users. In this paper, we formalize the FAIR-BATCH-MAB problem (Multi-Armed Bandit) as the above online batch recommendation with fairness constraint: the number of recommendations of each item must be at least [the specified minimum recommendation ratio of the item] \(\times \) #[user] \(\times t\) \(-\alpha \) in any round t, where \(\alpha \) is an unfairness tolerance constant. We show that this problem is represented as linear programming using an unknown set of click rate \(\{\mu _{i,j}\}\) if the reward for item-i recommendation to a user of the group j is 1(clicked) with probability \(\mu _{i,j}\) , and 0(not clicked) with probability \(1-\mu _{i,j}\) . We define regret by the expected total cumulative reward difference from the cumulative reward of the optimal solution of the linear programming. We propose the FBO (Fair Batch Optimizer) algorithm using the bandit algorithm as click rate estimators for the FAIR-BATCH-MAB problem. In simulation experiments based on a real-world dataset, we demonstrate that the performance of the FBO algorithm combined with Thompson Sampling is close to the performance of the optimal solution of the linear programming and outperforms the FBO algorithm combined with UCB or sample mean.