Aiming at the problem that the conventional single-screw has poor mixing and shearing performance due to its simple structure, a new graded single-screw structure was proposed by changing the number of threads and the root diameter of the screw based on the conventional single-screw. Using SolidWorks, models of the progressive single-screw and the conventional twin-headed single-screw were established. Based on the Finite Element Method (FEM), the two models were simulated and analyzed using Ansys. The results, such as pressure, shear rate, and residence time, were used to evaluate the performance of the graded single-screw. The results showed that the pressure peak within the flow field of the graded single-screw was approximately 4.7 times that of the conventional twin-headed single-screw, indicating a stronger pressure-building capability. The varying root diameter of the screw increased the shear rate in the flow field, resulting in better shearing performance. The increase in the number of threads of the progressive screw extended the residence time of the material in the flow field to 2.3 times that of the conventional twin-headed single-screw, leading to more uniform mixing of the material. The graded single-screw thus exhibited superior mixing performance. The study provides a basis for the optimization of the structure and improvement of the performance of single-screw extruders.