The transmission distance of a self-referenced continuous variable quantum key distribution (SR-CV-QKD) protocol still needs to be improved. Therefore, this study proposes an optical amplifier to improve the system and effectively compensate for the attenuation of phase noise caused by reference pulse. The secret key rate is derived through security analysis. Simulation results based on practical parameters show that adding an amplifier can improve the performance of the SR-CV-QKD protocol with a weak reference pulse and extend the maximum transmission distance.