As one of the three payloads of the Advanced Space-based Solar Observatory (ASO-S), the pre-launch characterization of HXI includes the characterization of the collimator and the spectrometer. This article focuses on the pre-launch characterization of HXI's spectrometer, including detection efficiency, energy resolution, and energy to ADC channel (E-C) relationship. The detection efficiency characterization necessitates a sufficient number of calibrated energy points in the HXI observation energy range, with a refined measurement around the absorption edge of the lanthanum bromide crystal, and is calibrated with an X-ray beam. The characterization results are consistent with the simulations and show that the detection efficiency difference between detector modules is controlled within ±3%. Radioactive sources 133Ba and 137Cs are used to calibrate the energy resolution and E-C relationship. The characterization results show that all detector modules' energy resolutions are better than 26% at 32 keV, meeting the design specification. And their E-C relationships vary regularly with voltage. All of the characterization results indicate that the flight model of the HXI spectrometer meets the performance requirements and is capable of performing on-orbit observation activities.