Coupling laser beam with plane wavefront into single-mode fiber (SMF) is a key technology in free-space optical communication. The influences between single-order wavefront aberration and atmospheric turbulences aberration on SMF coupling efficiency are analyzed in the Matlab simulation environment, respectively. The iteration courses of tilts correction using stochastic parallel gradient descent (SPGD) algorithm and their effects on coupling efficiency are studied. The simulation results show that SMF coupling efficiency drops with the increment of root-mean-square (RMS) value of single-order wavefront aberration, while the SMF coupling efficiency improves when the tilt aberrations of atmosphere are compensated. And the tilts are the main acting factor to SMF coupling efficiency when D/r0 is small. A closed-loop control system based on SPGD algorithm is established, where the adaptive fiber coupler (AFC) is employed to correct tilt aberrations of simulated turbulence. After tilt aberrations of simulated turbulence are corrected, the SMF coupling efficiency increases from 30.07% to 61.72% and the mean-squared-error (MSE) drops from 7.28% to 2.16%.