We investigate the teleportation between two relatively accelerating partners undergoing the phase flip, bit flip and bit-phase flip channels. We find that: 1) the fidelity decreases by increasing the acceleration of accelerated observer; 2) the dynamic evolution of the fidelity is different for various channels if the acceleration is fixed; and 3) the fidelity is always symmetric about β²=1/2 where βis a parameter of the transmission state.