•A model of microwave heating process with translational motion and rotation was built.•Implicit function and level set method are used to express the elements’ motion.•Effects of samples' moving speeds and shape on the heating uniformity are analyzed.•This method can analyze the industrial microwave heating process with complex motion. In practical chemical applications, in order to improve the microwave heating uniformity, moving elements, such as mode stirrers, turntables and conveyor belts, have been widely used as an easy way to implement. However, different moving elements may have different shapes, modes of motion and moving speed, which makes the simulation of the heating process very difficult. In this paper, a stepping algorithm based on implicit function and level set method is proposed to simulate the microwave heating process of multi-component with unequal moving speed. The accuracy of the algorithm is verified by discrete method and experiments. Moreover, the model was used to analyze the heating process with different components at different positions and speeds. The effect of different materials of mode stirrers and shapes of heated sample on heating process were also compared. The researches show that the proposed model can effectively improve the heating uniformity and heating efficiency.