The peak power of a battery is a vital feature for electric vehicles to maximize battery efficiency and ensure the safe operation of the system. Currently, the estimation and prediction of the state-of-power are based either on precise model algorithms or a large amount of test data. However, these methods will lead to conservative measurements. In this study, 11 Ah LiFePO4 cells are selected as the research object, and a new peak power test experimental procedure is proposed, which is mainly based on the constant power charge/discharge modes. Moreover, the conception of power sensitivity is proposed, which will make the procedure easier to determine the set power during the constant power experiments. The results indicate that the method can assist researchers in achieving a full understanding of the peak power characteristic of batteries.