In this paper, a new, to the best of our knowledge, scheme is proposed to mitigate the atmospheric turbulence effect in coherent free-space optical (FSO) communications with 8-quadrature amplitude modulation by employing amplitude compensation and phase recovery. The amplitude compensation and phase recovery algorithm in the scheme can significantly improve system performance without acquiring instantaneous channel state information or probability density function of a turbulence model. Numerical studies show that the bit error rate of the proposed scheme is four orders of magnitude lower than that of the system without any algorithm over a lognormal turbulence channel with normalized standard deviation of irradiance σ=0.25 and phase noise with normalized variance σϕ2=0.07, when the frequency offset fo=20MHz, combined linewidth Δf=10kHz, and average signal-to-noise ratio γ=20dB. Experiments are also carried out to investigate the performance of the scheme, and the results prove its superiority. Hence, this scheme can contribute to practical realization of the FSO system.