The average bit error rate (BER) performance of direct single-input multiple-output (SIMO) free-space optical link over correlated non-Kolmogorov turbulence fading channels is studied. In particular, the new closed-form expressions of BER performance of maximal ratio combining (MRC) and equal gain combining (EGC) receive-diversity systems are derived by α-μ distribution approximation method. The influence of both spectral power law and the channel correlation on the BER performance of MRC and EGC diversity systems is systematically investigated and compared. Monte Carlo simulation results are also presented to illustrate the validity of the proposed approach. We will help to investigate the fading correlation in spatial diversity systems and provide useful information for the design of the diversity system.