In this paper, a one-dimensional transient fluid model is used to investigate the asymmetric characteristics of the radio-frequency atmospheric-pressure helium glow discharges produced using a co-axial-type plasma generator. Based on the analysis of the particle and energy balance processes in the discharge region, the modeling results show that the asymmetric features of the time-averaged plasma parameters, e.g., the species number densities, electron energy and the electric field, become significant resulting from the increase in the discrepancy between the surface areas of the inner and outer electrodes. And the influence of the inner electrode radius on the asymmetric features of the discharges becomes more significant compared with the electrode gap spacing for the cases with smaller inner electrode radius. The calculated asymmetric features of the discharges are also validated by the experimental analysis on the discharge images using the visible image processing technique qualitatively.