In this paper, a time-varying controller is developed for Euler-Lagrange systems with bounded disturbances. A mapping strategy is designed to make the convergence time of the system achieve at an arbitrarily pre-assigned finite time. The selection of the time period is independent of the initial conditions, and the performances is free of chattering. To be specific, the proposed controller is constructed in two steps: Firstly, a common PD controller is designed to ensure the asymptotical stability of the nominal system; Secondly, by employing the mapping strategy, then the obtained new controller can make the disturbed system converged at a specified time. In the simulations, a two-link manipulator is used to validate that both uniformly stability for the undisturbed system and pre-assigned time attraction for the disturbed system can be achieved.