We report a method of femtosecond crystallography for solving radiation damage-free crystal structures of large proteins at sub-angstrom spatial resolution, using a large single crystal and the femtosecond pulses of an X-ray free-electron laser (XFEL). We demonstrated the performance of the method by determining a 1.9-Å radiation damage-free structure of bovine cytochrome c oxidase, a large (420-kDa), highly radiation-sensitive membrane protein.