Application of high T_c superconductors to accelerator magnets provides the following benefits. It reduces power consumption compared to copper magnets, it allows simple operation and less governmental regulation compared to low T_c superconductors because of the applicability of cryocoolers, and it is potentially more stable thermally, when operated at high temperatures where the specific heats of materials are large. An R&D project focusing on fundamental technologies for accelerator magnets using coated conductors is in progress, funded by the Japan Science and Technology Agency from January, 2010. Stage I of the project was completed successfully in March, 2012, and the project moved to the four-year Stage II in April, 2012. We aim to realize application of high T_c superconductors to magnets of strong-focusing accelerators for carbon cancer therapy or accelerator-driven subcritical reactors (ADSR). In Stage I, we conceptually designed a couple of fixed-field alternating gradient (FFAG) accelerators for carbon cancer therapy and for ADSR as well as a beam transport line for a carbon cancer therapy facility. Based on the conceptual designs of accelerators, coil-dominated magnets and iron-dominated magnets wound with coated conductors were designed. The required winding technologies were clarified through designing these magnets, and the R&D of winding technologies for coils with three-dimensional shape and those with negative bend have been carried out. The influence of the magnetization of coated conductors on the field quality of magnets was studied experimentally. The influence of the neutron radiation on the conductivity of aluminum and that of copper was also studied.