We demonstrate a hard-X-ray self-seeded (HXRSS) free-electron laser (FEL) at Pohang Accelerator Laboratory with an unprecedented peak brightness (3.2 × 1035 photons/(s·mm2·mrad2·0.1%BW)). The self-seeded FEL generates hard X-ray pulses with improved spectral purity; the average pulse energy was 0.85 mJ at 9.7 keV, almost as high as in SASE mode; the bandwidth (0.19 eV) is about 1/70 as wide, the peak spectral brightness is 40 times higher than in self-amplified spontaneous emission (SASE) mode, and the stability is excellent with > 94% of shots exceeding the average SASE intensity. Using this self-seeded XFEL, we conducted serial femtosecond crystallography (SFX) experiments to map the structure of lysozyme protein; data-quality metrics such as Rsplit, multiplicity, and signal-to-noise ratio for the SFX were substantially increased. We precisely map out the structure of lysozyme protein with substantially better statistics for the diffraction data and significantly sharper electron density maps compared to maps obtained using SASE mode.