The linear barotropic vorticity equation describing wind-driven ocean circulation is considered as a convection-diffusion equation that can be numerically solved by lattice Boltzmann method. Numerical experiments are carried out to examine the validity of the model for the wind-driven circulation. When horizontal viscosity is constant and spatially uniform, all numerical solutions for different parameters approach analytical solutions well. The spatially varying horizontal viscosity is also included in this model. It is shown that the variant horizontal viscosity increases the meridional transport significantly in west boundary current. By the investigation of numerical results, it was concluded that this model is competent for simulating western boundary current. The linear barotropic vorticity equation describing wind-driven ocean circulation is considered as a convection-diffusion equation that can be numerically solved by lattice Boltzmann method. viscosity is constant and spatially uniform, all numerical solutions for different parameters approach analytical solutions well. The spatially varying horizontal viscosity is also included in this model. It is shown that the variant horizontal viscosity increases the meridional transport significantly in west boundary current. By the investigation of numerical results, it was concluded that this model is competent for simulating western boundary current.