In this paper, simulation and time-optimal control of an electro-dynamic tether system as a new and inexpensive form of space propulsion system are investigated. The EDT, can provide desired acceleration by interaction between a current in the tether wire and earth’s magnetic field, without any fuel consumption, for any orbital maneuvering. For this reason, it is an appropriate choice for space debris mitigation missions. In this work, firstly, dynamics of the EDT, together with the earth’s magnetic field are simulated. Secondly, exploiting the developed simulation tool-set, variations of classical orbital elements are observed and then feasibility studies of non-impulsive orbital maneuvers are conducted. In this manuscript, distinctly, relative motion and rendezvous by means of the EDT, adoption of appropriate coordinate system, problem conditions and also the method of solution are discussed. Simulation results demonstrate that the EDT can perform a wide range of in-plane and out-of-plane orbital maneuvers in low-earth-orbits (LEO). Eventually, an in-plane rendezvous problem with space debris, is solved by implementation of Direct Collocation method in Matlab by developing a solver program and resolving its limitations with respect to optimal rendezvous problem using electrodynamic tether, and then optimal control in a minimum-time condition, and also optimal trajectory are obtained.