Aiming at the combined effects of geometric spreading and pointing errors on space optical links, the bit error rate (BER) performance of the all-optical amplify-and-forward(AOAF) relaying high altitude platform(HAP)-GEO-HAP communication links was researched. The GEO-based satellite AOAF relaying HAP optical communication link was modeled. The statistical characteristics of the channel fading index and the strength of the noises were investigated when the background radiation and the amplified spontaneous emission(ASE) noises were considered. With the help of the obtained Q factor of the proposed link model, the expression of BER was theoretically derived. The relationship between the BER performance and the bit rate under different parameters such as the transmitted optical power, jitter standard deviation and the beam-width was analyzed by simulation. The results show that, the BER performance is obviously improved by increasing the transmitted optical power, reducing the jitter standard deviation or decreasing the beam-width when the bit rate is low. On the other hand, a slight improvement of the BER performance is obtained with the same measures when the bit rate is larger than 4 Gbps.