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Aiming at the demand for high-capacity wireless-fiber link, the coupling efficiency of Laguerre Gaussian (LG) vortex beam into parabolic fiber under atmospheric turbulence is first investigated. The coupling model is established based on vortex mode analysis in free space and fiber. Effects of turbulence on coupling efficiency are analyzed, from which the way for system optimization is proposed to mitigate the efficiency decline. We find that LG beam with small OAM number, low radial index and long wavelength is able to achieve higher coupling efficiency in turbulent atmospheric conditions. As for the transmitting beam waist of LG beam or the focal length of receiving lens, there exist optimal values to realize size matching between spatial and fiber modes for coupling. The results are beneficial to the design of coupling system.