The Gaussian beam propagation theory is employed to analyze the effects of alignment errors including radial offset, end face tilt offset, and axial offset on the efficiency of coupling between the space light and single-mode fiber (SMF). The numerical and experimental results show that when the angle Ω between the end face and radial direction is 90° and 270°, the effects of the three alignment errors on the coupling efficiency are independent from each other. When the angle Ω is 180°, the coupling efficiency reaches the maximum value. To better compensate the influence of alignment errors on the SMF coupling efficiency, we design an optical fiber coupler with a 5 degree-of-freedom coupling structure on the basis of piezoelectric ceramics and the stochastic parallel gradient descent algorithm with a variable gain to find the optimal alignment attitude for coupling space light into SMF. The experimental results show that the 5 degree-of-freedom optical fiber coupler can effectively correct different alignment errors and that the SMF coupling efficiency reaches 53.2% when the system is in closed-loop state.