In the research of simulation for problems with large distortion in fluid dynamics, it is often required to re-construct the computational meshes. The technique transferring physical quantities between the two computatioal meshes is called as rezoning (remapping). Based on ENO interpolation idea, in this paper, a new kind of conservative ENO rezoning (remapping) algorithm is developed to structure and unstructured computational meshes. Finally, the numerical results show that the algorithm appears to be effective.