Vortex beams with orbital angular momenta with different mode numbers are mutually orthogonal to each other, which makes it possible to improve the information transmission efficiency in space optical communication system. Nevertheless, the implementation of this strategy is limited by the orbital angular momentum crosstalk caused by atmospheric turbulence. Focused Laguerre-Gaussian vortex beams are less affected by atmospheric turbulence due to their lager intensity density. Consequently, focused Laguerre-Gaussian vortex beams can be used as the carriers to reduce the orbit angular momentum crosstalk and increase the channel capacity of information transmission. In this paper, based on the spiral spectrum analysis theory, the analytical expression of spiral spectrum of focused Laguerre Gaussian beam propagating in anisotropic atmospheric turbulence is derived. The influences of turbulence and beam parameters on the received power of focused and unfocused Laguerre Gaussian beam are investigated via numerical calculations. Finally, the multi-phase screen method is used for verificating the simulation. The research findings are as follows. First, with the increase of transmission distance, turbulence intensity and topological charge, the receiving power of orbital angular momentum decreases, that is, the orbital angular momentum crosstalk turns more serious. Second, the larger the turbulence inner-scale, anisotropy index and beam wavelength are, the smaller the orbital angular momentum crosstalk is. Third, when the receiving aperture reaches a certain value, its influence on the orbit angular momentum crosstalk is very small. Fourth, different parameters have different effects on crosstalk, and the orbit angular momentum crosstalk of the focused vortex beam is less than that of the unfocused vortex beam. Therefore, in the vortex optical communication, the focused vortex beams can be used as the signal light to reduce the crosstalk between the orbit angular momentum modes, and thus improving the communication quality. These results have some theoretical reference values for reducing crosstalk in free-space optical communication.