Abstract: Helium atmospheric pressure plasma jets (He APPJs) have promising applications in many fields such as biomedicine and material processing. In this contribution, a 2-dimensional fluid model was constructed to study the physical mechanism of the cathode-directed propagation of a positive DC driven He APPJ. Influence of helium-air mixing layer and a small amount of air impurities in the discharge channel on the discharges was highlighted. The simulation results were in good agreement with the experimental observations, and it further showed that the change of electron collision ionization rate caused by the electron energy distribution in the He-air mixing layer played an essential role in the formation of cathode-directed streamer and the hollow-section ionization wave structure. Penning ionization can promote the discharge, but it has no decisive effect on the formation of the streamer and the ionization wave structure. A small amount of N₂/O₂ impurities in the discharge core channel show two competing effects of promoting the discharge via Panning ionization, or inhibiting the discharge via energy dissipation to molecule excitation and electron attachment to O₂.