Detecting replay attacks in power systems is quite challenging, since the attackers can mimic normal power states and do not make direct damages to the system. Existing works are mostly model-based, which may either suffer from a low detection performance or induce negative side effects to power control. In this paper, we explore purely data-driven approach for good detection performance without side effects. Our basic idea is to learn a classifier using a set of labelled data (i.e., power state) samples to detect the replayed states from normal ones. We choose the Support Vector Machine (SVM) as our classifier, and a self-correlation coefficient as the data feature for detection. We evaluate and confirm the effectiveness of our approach on IEEE bus systems. © 2017, Springer Nature Singapore Pte Ltd.