A network model has been investigated to understand the theological characteristic of complex fluids which form certain structures depending on thermodynamic or deformation history. The creation and loss rates of the crosslinks are given as an exponential function of effective strain, which is defined as a ratio of the first normal stress difference and the shear stress. Two empirical parameters are introduced in the model. Depending on the parameter values, the model predicts various cases including both shear thickening and shear thinning. A special case predicts the theological properties of a real fluid very well; an aqueous poly(vinyl alcohol) solution containing sodium berate. By considering as many cases as possible which are mathematically feasible, characteristics of each class have been studied and explained in terms of network parameters. The origin of shear thickening as well as the change of relaxation time and fluid elasticity have also been clarified with the help of network parameters. Even though this model does not cover all the real fluids and the description of the microscopic process is not sufficient, it helps us to increase our understanding of the characteristics of complex fluids as well as the mechanism of shear thickening.