Voltage sag is currently one of the most important power quality problems in power system, which has become increasingly a focus of attention in society. Due to the defects of traditional algorithm that has complex operation and poor precision, this paper proposes a voltage sag detection method based on complex impedance. Firstly, Hilbert transform is used to construct the analytic signals for detected voltage and current signals separately, and then their corresponding complex impedance will be calculated, making use of the specialty that when the voltage sag happened, its impedance and phase angle will jump at the same time, and combining overrun discriminator, the proposed method can locate the occurrence time of voltage sag, and detect its time duration. Finally, the effectiveness of the proposed method in this paper is verified by several experiments, the experimental results show that this method has high accuracy and easy to distinguish, it has wide promotional value.