The puncture of glass fibre reinforced polymer (GFRP) laminate is a primary damage pattern of wind turbine blades due to lightning strikes. A numerical simulation model of positive streamer propagation in a needle‐to‐plate air gap with a GFRP laminate is established to investigate the breakdown mechanism of GFRP laminate. The model not only considers the dynamics of charged particles in the air and the composite laminate, but also the current continuity at gas–solid interfaces. The simulated streamer discharge pattern and the surface streamer length are in good agreement with the observation results. The distributions and evolutions of the electron number density, electric field, and surface charge densities during streamer propagation are obtained. It is found that the enhancement of the electric field on the GFRP laminate is caused by the rapid deposition of positive and negative space charges on the GFRP laminate after a secondary streamer incepts on the lower surface of the GFRP laminate. The effects of the applied voltage, relative permittivity, and thickness of the GFRP laminate on the electric field on the GFRP laminate are investigated. The obtained results could assist in further understanding of the mechanism of GFRP wind blade breakdown due to lightning strikes.