Underwater optical communication has been a promising technology but is severely affected by underwater turbulence due to the resulting fluctuations in the index of refraction. In this paper, a revised spatial power spectrum model is obtained that considers the refraction index to be a function of the eddy diffusivity ratio, assuming the underwater turbulence is anisotropic. The scintillation indices for both plane and spherical waves that propagate in underwater turbulence are derived based on this model. Thereafter, the performance of an optical communication system, i.e., the outage probability and bit error rate, with the associated aperture averaging effect is considered. The simulation results demonstrate that temperature-induced and salinity-induced turbulence have distinct influences on the scintillation index and consequently result in different system performances. In addition, the variation in the eddy diffusivity ratio in some intervals induces more complicated results for underwater optical communication. Moreover, the effect of the receiver aperture diameter on the aperture averaging factor is presented in anisotropic underwater turbulence. Such an effect is more obvious in the plane wave case than in the spherical wave case. These results can find potential application in the engineering design of optical communication systems in an underwater environment.