Based on variable gain relays, the expression of outage probability lower bound for high altitude platform multi-hop optical communication is given. The effect of the factors, including atmospheric turbulence, tracking error and relay node position, on the performance of multi-hop optical links is analyzed. The simulation results show that the influence of atmospheric turbulence on optical links is lower than pointing error. The influence of relay node position on multi-hop optical links is related with tracking error. The bigger tracking error is, the stronger is the dependence of the position of relay node on optical links. The influence of relay node position on inter-high altitude platform (HAP) optical link will worsen and the performance of multi-hop optical links can be improved by the improvement of signal noise ration (SNR). Taking relay number of 2 and tracking error of 20 m as an example, outage probability of links reduces approximately by 2.2 dB while the average SNR per hop increases by 1 dB.