A cold-cathode penning-type ion source has been developed in our laboratory to study the electric breakdown in this type of sources. The breakdown voltage was measured as a function of axial magnetic field, in the range of 440-600 G, and anode length, in steps of 14, 20, and 24 mm. The measurement was performed with stainless steel cathodes in argon gas at pressure of 4 × 10(-2) mbar. Furthermore, a model was developed to explain the breakdown voltage data. In the construction of the model, the first Townsend coefficient was not directly used to avoid difficulties originating from the non-uniformity of the electric field. The empirical parameters of the model were obtained using the experimental data. The equation γ = c × (E(z)/N)(n), expressing the effective secondary emission coefficient in terms of reduced electric field, which was needed in the modeling process, was inspired from previous works. The parameters c and n were then calculated from the empirical parameters of the model. The n parameter turned out to be 0.59, which differs from the value reported by other authors merely by 1.6%. Three values, 0.010, 0.013, and 0.017 corresponding to the three anodes were obtained for the c parameter. These numbers are in good agreement with 0.01, which has been reported in the previous works. It was also found that the value of n has a decisive impact on the breakdown voltage curve in the high breakdown voltage region.