A MOVING GRID method is introduced in this paper and different motions of the body are simulated using this method. This study indicates that by regular and systematic change of GRID connections in some elements with regard to the size of the body’s motion, a MOVING-GRID can be obtained which is capable of being adapted to the large motions of the body without reducing the quality of elements. In order to model the rotational or translational motions of the body, cylindrical or elliptical shells from the elements around the body are taken into consideration to change the GRID connections. To indicate the correct performance of introduced MOVING-GRID method, several test cases including rotational and translational motions are solved. The Euler equations in the three dimensional unsteady form is solved using a dual time implicit approach. Numerical dissipative term using Jameson method is added to the equations. To accelerate convergence, local pseudo-time stepping, enthalpy damping and residual averaging are used. The results are validated with experimental or numerical data and excellent agreements among the results are observed.