A project of high energy heavy ion acceleration is under consideration. The high energy heavy ions can produce highly condensed states of nuclei. A new phase of nucleus would be seen at the incident energy higher than 140 MeV/nucleon. High energy heavy ions causing high density states and meson emission will produce various new nuclides. Process of formation of atomic elements will be studied. Various fields of science can be also investigated by the high energy heavy ions. Spectroscopic study of multi-valent ions will be made high energy uranium. Study of materials for the fusion reactor is important. Impurity heavy ion from the wall of the fusion reactor may lose the energy of the reactor, and the characteristic features of heavy ions should be investigated. The highly ionized states of atoms are also produced by heavy ion injection into material. Several projects of heavy ion acceleration are in progress in the world. The Numatron project in Japan is to construct a combination machine of a Cockcroft type machine, three linear accelerator and a synchrotron. The planned energy of the machine is 670 MeV/nucleon. Technical problems are under investigation.