The glow discharge in pure helium at atmospheric pressure, controlled by a dielectric barrier between coaxial electrodes, is investigated based on a one-dimensional self-consistent fluid model. By solving the continuity equations for electrons, ions, and excited atoms, with the current conservation equation and the electric field profile, the time evolution of the discharge current, gas voltage and the surface density of charged particles on the dielectric barrier are calculated. The simulation results show that the peak values of the discharge current, gas voltage and electric field in the first half period are asymmetric to the second half. When the current reaches its positive or negative maximum,the electric field profile, and the electron and ion densities represent similar properties to the typical glow discharge at low pressures. Obviously there exist a cathode fall, a negative glow region, and a positive column. Effects of the barrier position in between the two coaxial electrodes and the discharge gap width on discharge current characteristics are also analysed. The result indicates that, in the case when the dielectric covering the outer electrode only, the gas is punctured earlier during the former half period and later during the latter half period than other cases, also the current peak value is higher, and the difference of pulse width between the two half periods is more obvious. On reducing the gap width, the multiple current pulse discharge happens.