Based on the Rytov approximation theory, we analyze the cross-spectral density of Hankel-Bessel (HB) beams in anisotropic ocean turbulence. In this paper, we study the orbital angular momentum (OAM) mode detection probability, the crosstalk probability and the spiral phase spectrum of the HB beam, and establish the OAM mode detection probability model in anisotropic ocean turbulence. The results show that the detection probability of the emission mode is decreased and the spiral phase spectrum is expanded due to the ocean turbulence. Furthermore, with the increase of anisotropy factor, the influence of ocean turbulence on the detection probability of HB beam becomes smaller. Meanwhile, with the increase of the temperature variance dissipation rate and the equilibrium parameter, and the decrease of the dynamic energy dissipation rate, the influence of ocean turbulence on the orbital angular momentum transmission is increased.