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.