Atmospheric pressure glow discharge was observed in a surface discharge generator. The frequency of ac power supply is more than 9 kHz and the sinusoidal peak-to-peak applied voltage is 9 Ky. The electric field intensity in a kind of surface discharge generators is calculated with the boundary element method. Then a two-dimensional fluid model was used to simulate the ion trapping and electron trapping in a surface discharge just before the breakdown. The simulation results are in good agreement with our observation.