Chirped wideband pump and seed pulses are usually considered for backward Raman amplification（BRA） in plasmas to achieve an extremely high-power laser pulse. However, current theoretical models only contain either a chirped pump or a chirped seed. In this paper, modified three-wave coupling equations are proposed for the BRA in the plasmas with both chirped wideband pump and seed. The simulation results can more precisely describe the experiments, such as the Princeton University experiment. The optimized chirp and bandwidth are determined based on the simulation to enhance the output intensity and efficiency.
