In order to improve the performance of free space quantum communication system, based on the principles of phase sensitive amplifier(PSA) and phase insensitive amplifier(PIA), Gaussian modulated continuous variable quantum key distribution (CVQKD) with PSA and PIA at the receiver of quantum communication system is studied, deduces the corresponding security-key rate formula. When the signal wavelength is 810 nm, 1550 nm and 3800 nm respectively, the simulation analyzes the relationship between the security-key rate and the distance when the receiver adopts homodyne detection and heterodyne detection under the collective attack and individual attack, and compares the improvement effects of PSA and PIA on the system performance under the same conditions. The simulation results show that when the receiver adopts homodyne detection and heterodyne detection respectively in detection and heterodyne detection, the system has better performance when PSA and PIA are selected accordingly.