A mathematical model for transient flow of non-Newtonian heavy oil with dynamic radius and variable viscosity is established.The non-Newtonian transient pressure distribution of heavy oil is obtained with time and space.It shows that under same production,dynamic radius is closer to the well as threshold pressure gradient increases.The greater the threshold pressure gradient, the greater the pressure drop neflr the well.We combine dynamic radius and viscosity to avoid shortcomings of existing non-Newtonian heavy oil flow model.