Understanding the damage mechanisms of fiber-reinforced polymer matrix composite materials under high voltage conditions is of great significance for lightning strike protection and high voltage insulation applications of composite structures. In this paper, we investigated effects of the lightning impulse (LI) voltage and high voltage alternating current (HVAC) puncture on damage modes of the electrically nonconductive glass fiber-reinforced polymer (GFRP) matrix composite materials through experimental tests and numerical simulations. The LI and HVAC tests represent the lightning strike and high voltage insulation cable puncture conditions, respectively. Our experimental examinations showed that GFRP composite specimens subjected to the LI voltage test exhibited distinct damage modes compared with those in the HVAC puncture test. The GFRP composite material suffered more charring and fiber vaporization in the HVAC puncture test, whereas less matrix charring and fiber vaporization but severe fiber breakage and delamination in response to the LI voltage tests. The findings indicate that the thermal effect dominates the damage of GFRP composites inflicted by the HVAC puncture test, whereas the mechanical impact effect governs the GFRP composite damage in the LI voltage test. In addition, the electric arc plasma formation during the puncture of the GFRP composite material was modeled through solving Maxwell’s equations and the heat generation equations using finite element analysis. Simulation results provided insights on the effects of duration and intensity of the high voltage electric discharge on the composite damage. © The Author(s) 2020.