This paper treats control strategy for tether-based method of damping angular momentum of failed satellites. A simple two-dimensional model of a tether, a controller and a circular/elliptic target is used for numerical simulations in order to gain clear understanding of the tether control. Several tether control methods are proposed using tension, length of the tether and the distance between the target and the controller. Numerical simulations yield the following results : 1)the tether tension can transfer from the angular momentum of the target to that of the controller ; 2)if the target is circular, the angular momentum of the target is reduced linearly using by constant tension control ; and 3)relationships between the target angular momentum change and model parameters are obtained.