Polymer fibre surface modification by low temperature plasma has received much attention in recent years. The plasma kinetic behaviour and reactive species distribution can be totally different with the existence of fibre. In this work, a 2D axisymmetric fluid model is established to study the interaction between an atmospheric pressure plasma jet and single fibre with different relative permittivity (εr=1.5 and εr=80, respectively). Dividing of the ionization wave is observed when approaching to the fibre, followed by fully wrapping of fibre surface. Afterwards, the ionization wave travels across the fibre and continues to propagate forward. Significant effects induced by the variation of the fibre’s permittivity are observed. For εr=1.5 fibre, the high electric field region shifts from the south pole (SP, closer to the jet tube) to the north pole (NP, opposite side to the SP), but the high electric field region remains at the SP for εr=80 fibre. This is due to the large potential difference on the εr=1.5 fibre surface. Furthermore, the time averaged surface fluxes of the main ions (He+, N2+ and O2+) and excited species (Hes, N and O) are analysed. It is found that the surface fluxes of εr=80 fibre at the NP is significantly higher than that of εr=1.5 fibre. Therefore, increasing the relative dielectric constant of fibre would increase the main ions and excited species surface fluxes at the NP.