Faster-than-Nyquist (FTN) transmission technology can effectively improve the transmission rate of free space optical communications. Unfortunately, the inter-symbol interference (ISI) introduced by FTN greatly affects the system reliability. To this issue, a point-by-point elimination adaptive pre-equalized algorithm is proposed. The theoretical bit error rate and computational complexity under 4 order pulse amplitude modulation are derived. The simulation results show that this algorithm can eliminate the ISI brought by FTN pulse shaping filter, and its performance is almost equal to that of orthogonal transmission system. In addition, the system computational complexity is inversely proportional to the acceleration constant. When the acceleration constant is less than 0.4, the computational complexity increases rapidly.