PEEK (polyetheretherketone) and N 2 are used in the packaging of high-voltage power electronics as the frame material and insulation gas, respectively. The surface discharge behaviours of PEEK in N 2 under positive repetitive square voltage are the main concerns for the packaging insulation design. However, the influence of N 2 pressure on discharge characteristics and mechanisms has not been investigated. Herein, the optical images of streamer propagation and surface discharge current pulses of PEEK in N 2 with different pressures are obtained under positive repetitive square voltage. The effects of different N 2 pressures on the surface discharge initial voltage (SDIV), pulse parameters of discharge current, time lag of discharge and streamer propagation length are analysed in detail. The effects of N 2 pressure on the memory effects of residual charges during surface discharge, effective ionisation rate and electron desorption rate are revealed. Furthermore, the time lag theory is used to analyse the influence of N 2 pressure on the time lag of forward and backward discharge. The effects of N 2 pressure on pulse parameters of discharge current, surface discharge initial voltage and streamer propagation length are also explained on the basis of the process of surface charges accumulation under different N 2 pressures. The presented results can provide guidance for the packaging of press pack IGBT (insulated gate bipolar transistor) and reveal the surface discharge mechanism with different N 2 pressures under positive repetitive square voltage.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.