During the air flow twisting process of jet vortex spinning, the moving characteristics of flexible free-end fiber are complex. In this paper, the finite element model of the fiber is established based on elastic thin rod element. According to the air pressure and velocity distribution in the airflow twisting chamber of jet vortex spinning, this paper analyzes the undetermined coefficients of the finite element kinetic differential equation of the free-end fiber following the principle of mechanical equilibrium, energy conservation, mass conservation and momentum conservation. Based on numerical simulation, this paper gets the trajectory of the free-end fiber. Finally, the theoretical result of the free-end fiber trajectory by finite element simulating is tested by an experimental method. This paper has proposed a new method to study the movement of the fiber and learn about the process and principle of jet vortex spinning.