A simple spectrometer using diffraction from diamond microcrystals has been developed to diagnose single-shot spectra of X-ray free-electron laser (XFEL) pulses. The large grain size and uniform lattice constant of the adopted crystals enable characterizing the XFEL spectrum at a resolution of a few eV from the peak shape of the powder diffraction profile. This single-shot spectrometer has been installed at beamline 3 of SACLA and is used for daily machine tuning.