In a particular condition, moving elements are typically used to improve heating uniformity during microwave heating. However, due to the complexity of mathematical models, the simulation of moving elements during microwave heating process remains a challenge. In this paper, a novel continuous algorithm based on Arbitrary Lagrangian-Eulerian method is developed to compute this heating process. By introducing the ALE method, the mesh of moving domain are set as a function of space coordinate and time, the mesh of surrounding domain is free deformation under the action of the moving domain, ensuring the accuracy and continuity of calculation by remesh the deformed configuration. A 2-D model and a 3-D model with a rotating turntable are used to illustrate the proposed method in detail. The change of temperature was measured by experiments to verify the rationality and accuracy of the proposed method. This method can be used in microwave heating simulation of other food movements and assist microwaveable food product development. (C) 2019 Published by Elsevier Ltd.