Abstract: A theoretical model and the finite element method (FEM) are used to simulate the durotaxis movement of the cell on an artificial substrate with a continuous varying stiffness for the test design. The viscoelastic properties of the cell and the dynamic reactions of the receptors and the ligands between the cell and the substrate, are all considered. The time step equal to that of producing a pair of receptor-ligand is used for discretizing the functions of the time, turning the dynamic FEM into a static one. And a condition of moving constraint for the cell structure is proposed for eliminating the singularity of the FEM matrix more easily. The simulation results show that there is a rapid fluctuation of the force in the focal adhesion during the cell durotaxis, the speed of the cell migration, as is consistent with the observation, and the migration process can efficiently last over 20 hours.