Benefiting from the rapid development of fiber-optic devices, high-speed free-space optical communication systems have recently used fiber-optic components. The received laser beam in such a system couples into single-mode fiber (SMF) at the input of the receiver module. This work is oriented to common problems in actual free-space optical coupling systems, such as atmospheric turbulence, optical system aberration, and fiber positioning error. We derive the statistical expectation models of SMF coupling efficiency with optical system aberration in the presence of atmospheric turbulence and the statistical expectation models of SMF coupling efficiency with fiber positioning error in the presence of atmospheric turbulence. The influences of optical system aberration and fiber positioning error on the coupling efficiency under different turbulence strengths are also analyzed in this paper.