Partial discharge (PD) is an important metric for the insulation diagnosis of power equipment. However, its detection is affected by the strong electromagnetic interference generated by pulse square voltage. We therefore propose a power interference suppression method for partial discharges under pulse square voltage based on a quadratic measurement method. We conduct analysis of the topology circuit when partial discharge occurs in the insulation test sample and introduce the basic principle of the secondary measurement method according to the superposition principle and the linear relationship between the square voltages at different peak values. We verify the feasibility of this method by simulating a PD signal with power interference. Subsequently, we use the successive interception comparison method to solve the non-correspondence of the two initial measurement points problem and design and manufacture the transformer turn-to-turn oil-paper insulation test sample and experimental tank. By measuring the PD starting voltage of the insulation test sample under the power frequency voltage, we determined the first measurement voltage under the pulse square voltage and obtained the signal x1(t) to subsequently measure the PD signal x2(t). According to the proposed successive interception comparison method, the signal x1(t) is processed, and the secondary measurement method suppresses the power interference of the measured signal x2(t). We demonstrate that the proposed method effectively suppresses the power interference in PD detection under a pulse square voltage.