Aiming at the combined effects of the GammaGamma atmosphere turbulence, geometric spread and pointing errors on space optical links, the bit error rate (BER) performance of the high altitude platform (HAP) OFDM optical communication link is investigated. The HAP OFDM optical communication link model based on MQAM is built, and the electrical carrier to noise ratio for OFDM optical communication link is obtained. The closed form mathematical expression for the total average BER performance is theoretically derived. The relationship between the BER performance and the transmitted optical power under different parameters such as the atmosphere turbulence, the normalized jitter standard deviation and the normalized beamwidth is analyzed by simulation. The results show that, the BER performance is obviously improved by increasing the transmitted optical power when the atmosphere turbulence condition is weak, or when the normalized jitter standard deviation is less than 0.6. On the other hand, no obvious improvement of the BER performance is obtained by increasing the transmitted optical power under different MQAM or normalized beam width.