Vanadium redox flow battery (VRB) is one of the most promising batteries at present. In order to enhance the stability and anti-interference ability of VRB in microgrids, a novel learning-based data-driven H∞ control approach is proposed for the VRB, which uses a new integral reinforcement learning algorithm to produce excellent steady-state and dynamic responses only by measurements. Compared to the model-based control methods, it is insensitive to model parameter variations. Furthermore, compared to most of the existing artificial intelligent control approaches that require large amounts of experimental data for offline neural network (NN) training, the proposed control strategy contributes to eliminate the offline training process and therefore, does not need the costly and tedious training data acquisition process. More importantly, the proposed control offers guaranteed closed-loop control stability, which cannot be achieved by nearly all the control methods that purely rely on the offline trained NNs. In this paper, the rigorous proof of stability is given, and the validity of the proposed method is verified by simulation results.