Abstract: A shear viscosity model of polymer melt is proposed based on a quadric Bezier curve to improve the model's descriptive precision. The model is characterized by piecewise functions in a logarithmic coordinate. Linear functions are adopted to represent the two linear sections of the Newton region at lower shear rates and the power law region at higher shear rates. A quadric Bezier curve is applied to describe the transitional region between the two linear regions. The three curves are connected smoothly by a control polygon which is formed through the extension lines of the two linear curves of the Newton region and the power law region. At any temperature, the end point of the Newton region at lower shear rates and the start point of the power law region at higher shear rates are predicted accordingly. The data fitting examples show that the precision of the proposed model turns out to be obviously higher than that of the Cross-Arrhenius model.