This paper presents the experimental and numerical results about the influence of nitrogen (N2) and oxygen (O2) admixture on the development of a helium (He) atmospheric-pressure plasma jet (APPJ) in a long dielectric tube. The results revealed that the jet length and the propagation velocity are strongly affected by introducing N2 or O2 into the He flow. Specifically, it was observed that a higher N2/O2 admixture led to the decrease in the density of both energetic and relative low-energy electrons outside the grounded electrode, which corresponds to the shortening of the jet length. In the He/O2 mixture, the electrons are easily captured by O2/O in the region of the plasma bulk. In the He/N2 mixture, the jet propagation characteristics will change since N2 has many low-level excitation states that consumed a large number of energetic electrons. The simulation shows that the magnitude of the axial electric field in the jet head depends strongly on the amount of N2 and/or O2 in the gas flow. In both cases, the peak electric field is on the order of 5 kV/cm, which is significantly higher than that in pure helium of 3 kV/cm even if the admixture is low (less than 4% N2 or 2% O2 in this work). Positive charges of higher density in the jet head are needed to induce a stronger electric field for the jet propagating in N2(x%)/He and O2(x%)/He mixtures compared with that in pure He.