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Atmospheric pressure glow discharge is observed for the first time in a surface discharge generator in flowing helium. Electrical and optical methods are used to measure the characteristics of atmospheric pressure glow discharge for different voltages. The results show that discharge current waveforms are asymmetric for the different polarities of the applied voltage. A continuous discharge profile with a width of several microseconds appears for per half cycle of the applied voltage when the voltage is increased to a certain value. The short-pulsed discharge and the continuous current would result from the Townsend breakdown and glow discharge mechanisms respectively. The properties of surface discharge in stagnant helium are completely different from that in flowing helium.