This study proposes a matrix-injection method to complete the H∞ performance analysis of linear systems under aperiodic sampled data. First of all, an augmented looped-functional is constructed by combining the looped-functional method with state vector augmentation. To make use of sampling period-related information in this augmented functional, sampling period-dependent quadratic terms are kept in the derivative of the functional. Then, to deal with the aforementioned quadratic terms, a matrix-injection method is developed. This method introduces two free matrices, which allows for a reduction in the conservativeness of the results. A sufficient condition with less conservatism is provided using these techniques. Finally, three examples are given to demonstrate the superiority of the presented approach.