The Advanced Space-based Solar Observatory (ASO-S) is one of the projects within the framework of the strategic priority program stage II (SPPII) on space science of the Chinese Academy of Sciences. The most important scientific goals of ASO-S are to study the relationships between the solar magnetic field, solar flares, and coronal mass ejections (CMEs). The Hard X-ray Imager (HXI) is one of the three payloads onboard ASO-S, it can obtain high spatial resolution and high cadence solar spectral imaging observations by Fourier modulation imaging of hard X-ray emitted by solar flares. The spectrometer is a core component of the HXI, whose main task is to precisely measure the energy and flux of solar hard X-ray passing through a grating pair. This paper presents the principle, key requirements, calibration equipment, and calibration scheme of the spectrometer. Finally, the calibration results are given to verify the correctness of the design of the spectrometer.