Recent developments of high Tc coated superconductor ((RE)BCO coated conductor) lead to the possibilities of very high field magnets operated at low temperature (~4.2 K) and efficient magnets operated at high temperature (several tens of Kelvin). For accelerator applications, however, the use coated conductors has been considered difficult due to their tape shape. A project funded by Japan Science and Technology Agency is in progress to challenge the difficulties and to develop the fundamental technologies of accelerator magnets using high Tc superconductors under close collaboration between Japanese university / national laboratories and industry. The primary applications are FFAG accelerators for carbon cancer therapy and those for accelerator-driven subcritical reactor. First, the overview of the project is summarized, and, then, recent results of research and development on several key issues for applications of high Tc superconductor tapes to magnets for FFAG accelerators are presented. This work was supported by Japan Science and Technology Agency under Strategic Promotion of Innovative Research and Development Program.