In space downlink coherent laser communication systems, the laser linewidth will affect the performance of the communication systems. The narrow linewidth laser can effectively reduce the laser phase noise caused by the laser linewidth and is the prime preference for present-day coherent laser communication systems. When optical signals are propagated in atmosphere channels, atmosphere turbulence will cause optical signals strength and phase fluctuations, which further affects the communication performance of the system. In response to the above problems, this manuscript derives the BER model for space downlink Quadri Phase Shift Keying (QPSK) communication system based on the principle of the QPSK communication system and further considered the linewidth of narrow linewidth laser, the fluctuation of optical signal intensity and phase fluctuations caused by atmosphere turbulence. Based on this model, the effect of narrow linewidth laser on the performance of space downlink coherent laser communication system under different atmosphere turbulence and communication rates is analyzed by numerical simulation. The results show that atmosphere turbulence not only severely affects the system performance but also weakens the effect of laser linewidth on the system performance. And the phase fluctuations caused by atmospheric turbulence have a greater effect on system performance than the light intensity fluctuations they cause. In addition, as the communication rate increases, the performance of the system decreases, and the laser linewidth has a reduced effect on the system performance. This paper has the practical reference for the optimal design and adjustment of space downlink coherent laser communication systems.