In this paper, the basic properties of the atmospheric pressure Ar plasma jet with three different electrode structures are comparatively studied using a two-dimensional axisymmetric fluid model. The results show that the introduction of the grounded ring electrode affects the jet propagation both inside and outside the dielectric tube. Inside the dielectric tube, the grounded ring electrode increases the radial electric field near the inner surface of the tube, leading to the increase of the electron density and jet propagation length. However, it has a slight effect on the electric field and electron density near the central axis. Outside the dielectric tube, the introduction of the grounded ring electrode results in the reduction of the electric field both in axial and radial directions. This inevitably causes the decrease of the jet propagation length and a contraction of the jet channel radius. For the bare needle electrode structure, the removal of the medium wrapped around the needle electrode increases the electric field due to the elevated plasma potential. This makes the increase of the jet propagation length. The peak electron density in the jet channel increases about one order of magnitude. Meanwhile, the electron density in the whole channel is relatively higher in the bare needle electrode structure. In addition, the production and transport of the main active particles under the three electrode structures are comparatively studied.