［Purposes］ The Cahn-Hilliard-Navier-Stokes equations, which are coupled by incompressible Navier-Stokes equations and higher-order anisotropic Cahn-Hilliard equations, are widely used and play an important role. ［Methods］ Bounded absorbing sets and uniform compactness of solution semigroup to the equations are obtained by using energy estimates. ［Findings］ Then the existence of attractors are proved according to the existence theorem of attractor. ［Conclusions］ The large time behavior of the equations under Neumann boundary condition for relative concentrations is studied.