We investigate the entanglement dynamics of two cavities interacting respectively with reservoir in non-inertial frames. We consider not only the influence of acceleration, but also the influence of different rates between right and left components of the Unruh single-particle state on entanglement. The result shows that the reservoir-entanglement will increase with the decrease of the cavity-entanglement when the acceleration parameter is fixed. In addition, there appears the redistribution of entanglement between particle mode and antiparticle mode, when the initial state is in a maximal by entangled state with |qR|=1. We also find that the sudden death of entanglement happens in infinite acceleration limit when |qR|=|qL|=1/√2, whereas the death of entanglement happens at finite acceleration when qR2.