A coupling efficiency calculation method for a Bessel-Gaussian (BG) beam in a free space optical communication system received by a parabolic Cassegrain antenna and coupled into a few-mode fiber is proposed. The system of the antenna and the coupling lens is approximate to a ring-shaped lens. The effect of the antenna in the coupling system is analyzed, and maximum coupling efficiency is increased by 76.25% on average by applying the antenna. With the application of the antenna, the configurations to generate the maximum point of coupling efficiency among BG beams of different topological charges are restricted to being almost the same, which is useful for the simultaneous propagation of multiple BG beams. The effects of radial displacement and atmospheric turbulence on coupling efficiency are researched as well. Coupling efficiency becomes more sensitive to radial displacement, while the influence of turbulence on coupling efficiency remains almost the same after applying the antenna. Our calculation method has an average absolute error of only 0.6625% while increasing the calculation speed greatly, which is practical for further studies of vortex beams.