We have developed an on-line spectrometer for hard x-ray free-electron laser (XFEL) radiation based on a nanostructured diamond diffraction grating and a bent crystal analyzer. Our method provides high spectral resolution, interferes negligibly with the XFEL beam, and can withstand the intense hard x-ray pulses at high repetition rates of >100 Hz. The spectrometer is capable of providing shot-to-shot spectral information for the normalization of data obtained in scientific experiments and optimization of the accelerator operation parameters. We have demonstrated these capabilities of the setup at the Linac Coherent Light Source, in self-amplified spontaneous emission mode at full energy of >1 mJ with a 120 Hz repetition rate, obtaining a resolving power of E∕δE > 3 × 10⁴. The device was also used to monitor the effects of pulse duration down to 8 fs by analysis of the spectral spike width.