Hollow cathode discharge and micro-hollow cathode discharge have numerous applications in the fields of industry, medical treatment, environmental protection, and analytical chemistry. However, many of them lack the typical features of hollow cathode mode, especially the applications at atmospheric pressure. In order to investigate the underlying basic science of hollow cathode discharge, the hollow cathode discharge in argon was studied by experiments. The range for the operation of the hollow cathode mode in the argon-aluminum device was quantitatively determined to be from 0.8 to 4 Torr cm, no matter how small the cathode cavity is. The atmospheric pressure operation of the hollow cathode mode was realised with the aluminum cathode of a 50 μm cavity. The hollow cathode discharges were consistent with Townsend similarity law when the anode was very close to the cathode and the value of p•D was chosen at the lower limit of the range for hollow cathode mode. In contrast, if the anode was moved a little bit far from the cathode and the value of p D was significantly increased, the results followed Allis-White scaling law. The reason for the deviation of Allis-White scaling law from Townsend similarity law was given.