Dynamic and thermodynamic behavior of associating fluids play a crucial role in a variety of engineering and science disciplines. Cubic plus association equation of state (CPA EOS) is implemented in a central-moments-based lattice Boltzmann method (LBM) in order to mimic the thermodynamic behavior of associating fluids. The pseudopotential approach is selected to model the multiphase thermodynamic characteristics such as reduced density of associating fluids. The priority of central moments-based approach over multiple-relaxation-time collision operator is shown by performing double shear layers. The integration of central-moments-based LBM and CPA EOS is useful to simulate associating fluids at high flow rate conditions, which is extended to high-density ratio scenarios by increasing the anisotropy order of gradient operator. In order to increase the stability of the model, a higher anisotropy order of the gradient operator is implemented; about 34 present reduction in spurious velocities is noticed in some cases. The type of gradient operator considerably affects the model thermodynamic consistency. Finally, the model is validated by observing a straight line in the Laplace law test. Prediction of thermodynamic behaviours of associating fluids is of significance in biological processes as well as fluid flow in porous media.