The gas pressure dependence of breakdown voltages of a micro-hollow cathode discharge is investigated.Experiments were carried out on a cylindrical hollow cathode,0.5 mm in diameter and 3 mm in depth in wide range of gas pressure of helium and its mixtures.Calculated Paschen curve based on Townsend theory were compared with the experimental results.The influences of admixed hydrogen and water vapor on the breakdown voltage ware considered by the modification of the ionization coefficient.The ionization by Penning collision between a hydrogen molecule and a helium excited atom is included by the addition of excitation coefficient to the ionization corefficient.The electron attachment with a water vapor is treated as the decrease of electrons contributive to ionization and the decrease of positive ions to the cathode surface contributive to the secondary electron emission.