With the characteristics self-focusing, the partially coherent Airy beam can efficiently limit the adverse effects of ocean turbulence, which negatively affects the coupling performance of space light and fiber. In this paper, the generalized Huygens-Fresnel principle and the partial coherent optical cross-spectral density function are used to derive the analytical expression of the coupling efficiency of partially coherent Airy beam-few-mode (four-mode) fiber through ocean turbulence. The effects of light source parameters, coupling parameters and ocean turbulence intensity on coupling efficiency are numerically analyzed. The results show that the coupling efficiency gradually decreases with the increase of wavelength, initial radius, truncation factor and coherence length, and gradually decreases with the enhancement of ocean turbulence. At different transmission distances, the best coupling parameters are given, so that the coupling of partially coherent Airy beams and four-mode fibers achieves the best effect.