The effects of the frequency on the electrical characteristics in a dielectric barrier discharge in pure helium excited by repetitive voltage pulses with the frequency from 5 to 500 kHz are systematically investigated by means of a 1-D fluid model under different operating conditions, including gap width , secondary electron emission coefficient , dielectric thickness , and dielectric constant . The important characteristic quantities of describing the pulse discharge, i.e., discharge current density , averaged electron density , averaged dissipated power density , and the axial distributions of both electron density and electron temperature , are calculated and analyzed in detail. This paper gives the following significant results. increases with increasing and is almost proportional to . Especially, there is a characteristic frequency of , namely, when is lower than , (peak value of in the first discharge) decreases evidently with increasing , and then changes very slightly for larger than . In addition, with the increase of , (peak value of in the second discharge) increases very slightly for small and the reverse is true for large . The frequency dependence of for different is similar to that by changing . For a fixed frequency, the change of with is very small, which differs from that at low frequencies. In addition, and decrease with increasing and increase with increasing , but there are almost constant and for high frequencies. When the frequency is larger than , there will be the second peak of outside the cathode sheath in the first discharge, and both large and small can result in the formation of the evident peak of nearby the momentary anode. It should be noted that the analysis in this paper pertains only to the incompressible motion of the plasma.