In this paper, general motion of a two-dimensional body is modeled using a new moving mesh concept. Solution domain is divided into the three zones. The first zone, with a circular boundary, includes the moving body and facilitates the rotational motion of it. The second zone, with a square boundary, includes the first zone and facilitates the translational motion of the body. The third zone is a background grid in which the second zone moves. With this configuration of grids any two-dimensional motion of a body can be modeled with almost no grid insertion or deletion. However, in some stages of motion we merge or split a few number of elements. The discretization method is control-volume based finite-element, and the unsteady form of the Euler equations are solved using AUSM algorithm. To demonstrate the excellent performance of the present method two moving cases including rotational and translational motions are solved. The results show excellent agreement with experimental data or other numerical results.