In our previous work, we have improved the reversible network model proposed by Cifre and co-workers, and performed a Brownian dynamics simulation to investigate the capability of the model in predicting the shear and elongational properties of non-associative polymeric fluids. In the present work, the capability of the improved model in predicting the rheological properties of associative polymeric fluids is presented. Similar to that for non-associative polymers, substitution of Hookean connection force with FENE connection force is required for better prediction in shear and elogational properties of associative polymer. In shear flow, the model with FENE connection force predicts shear thickening in the shear viscosity, and the peak of the shear thickening depends strongly on the maximum extension parameter. The responses in the first normal stress difference show that the model is able to predict relatively fast growth at low shear rates and relatively slow growth at high shear rates. In the elongational flow, the model is able to predict elongational viscosity with strain thickening at low strain rate followed by strain thinning or constant viscosity at moderate and high strain rates depending on various model parameters.