In this paper, the non-linear tranverse vibration of an axially moving pile-yarn with time-dependent tension are investigated. The pile-yarn material is modeled as Kelvin-Voigt element. A partial-differential equation governing the transverse vibration is derived from the Newton’s second law. The Galerkin method and the fourth order Runge-Kutta method are used to solve the governing non-linear differential equation. The effects of the transport speed, the tension perturbation amplitude and the damping coefficient on the dynamic behaviour of the system are numerically investigated.