Labyrinth-honeycomb seals are a state-of-the-art sealing technology commonly used in aero-engine interstage seal. The undesirable severe rub between the seal fins and the honeycomb due to the clearance change may induce the cracking of the seal fins. A pervious study investigated the wear of the seal fins at different radial incursion rates. However, due to the axial thrust and mounting clearance, the axial rub between the seal fins and the honeycomb may occur. Hence, this paper focuses on the influence of the axial rub added in the radial rub on the wear of the seal fins. The rub tests results, including rubbing forces and temperature, wear rate, worn morphology, cross-sectional morphology and energy dispersive spectroscopy results, are presented and discussed. Overall, the participation of the axial rub leads to higher rubbing forces, temperature, and wear rate. The tribo-layer on the seal fin is thicker and the cracks are more obvious at high axial incursion rate. These phenomena indicate the axial rub has a negative influence on the wear of the seal fins and should be avoided.