Abstract: The simulation for non-Newtonian fluid has been an important research topic in physically based fluid animation. In this paper, we propose a novel predictive-corrective algorithm for non-Newtonian fluid based on incompressible smoothed particle hydrodynamics(ISPH). First, the viscous liquid is modeled by a non-Newtonian fluid flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross model. Then, a predictive-corrective method is proposed, by correcting density error with individual stiffness parameters for each particle, to avoid tensile instability and improve numerical stability. Finally, a global adaptive time-stepping method is adopted, which adjusts the time step automatically independent of the scenario and improve efficiency significantly. The results show that the proposed method can model the Newtonian fluid and the shear thinning non-Newtonian fluid, remove the tensile instability, and simulate in larger time step.