In this paper, Euler equations are solved to simulate compressible flow on unstructured moving grids. Solution domain is discretized using control-volume finite-element method. This method is benefited from the power of finite element in discretizing solution domain, and the capability of finite volume in conserving physical quantities. For the evaluation of flux vector components at the control-volume surfaces, we employed the flux-difference scheme of Roe, modified for moving grids. Geometric conservation laws are implemented carefully to prevent solution errors produced by grid movement. To demonstrate the accuracy of the algorithm in solving fluid flow problems on moving grids, a number of test problems have been carried out.