To explore the relationship between the local oscillator power and the coherent detection sensitivity in free-space coherent optical communications, the mathematical model about the influence of the local oscillator power on the sensitivity of coherent detection was established, and the effect of local oscillator power on the sensitivity of coherent detection under different parameters was simulated. The coherent detection sensitivity testing system was set up by using the high-speed and large-area space-coupling balanced detector produced from Wuhan University, then the effect of the local oscillator power on the detection sensitivity was verified experimentally. The experimental results show that the detection sensitivity is always affected by the intensity noise of the local oscillator due to the dismatch of the two photodiodes in the coherent detection system; thus there exist an optimal local oscillator power which can realize the maximum value of coherent detection sensitivity with certain environment parameters of the detector. When the bit error rate is 10-12 and the communication rate is 5 Gbps, the maximum value of the coherent detection sensitivity in the test is -40.16 dBm and the corresponding optical power is 9 dBm. The proposed model has an guiding significance for the improvement of detection sensitivity of coherent detection systems.