With the development of next-generation reactors, the demand for higher precision in nuclear data has increased significantly to ensure operational efficiency and safety. Especially, inelastic scattering cross-section is one of the key parameters in nuclear reactor physics calculations, which directly affects neutron economy, thermal-hydraulic design, and safety analysis. Stainless steel is widely used in the nuclear industry. Chromium (Cr) is one of the main alloying elements in stainless steel, and ⁵²Cr is the most abundant isotope in nature. However, the measurement of the inelastic scattering cross-section of ⁵²Cr has not been explored in China, so the study of the ⁵²Cr (n, n′ γ) reaction cross-section is crucial for nuclear reactor calculations. In this study, the neutron beams with energies of 5.62, 6.24, and 7.95 MeV via the D (d, n) ³He reaction are generated from the HI-13 tandem accelerator at the Institute of Atomic Energy in China. These neutrons are used to bombard a ⁵²Cr target. Four CLOVER detectors are located at 30°, 70°, 110° and 150° relative to the beam direction in the horizontal plane. The prompt γ-ray method is used to measure the inelastic scattering cross-section by using an HPGe detector array. This is the first time that the cross-sections of five inelastic γ-rays with energies of 647.47 keV, 935.54 keV, 1333.65 keV, 1434.07 keV and 1530.67 keV have been obtained experimentally in China. Additionally, theoretical model calculations are performed to determine the inelastic scattering cross-sections of neutrons with energies below 20 MeV interacting with ⁵²Cr. In the analysis of the experimental data, γ-ray self-absorption correction, neutron flux attenuation and multiple scattering correction are considered. The total experimental uncertainty includes the measurement uncertainty, correction term uncertainty, and standard cross-section uncertainty. The results show that the γ-ray production cross-sections obtained at the three neutron energy points are in good agreement with the data measured by Mihailescu et al. [Mihailescu L C, Borcea C, Koning A J, Plompen A J M 2007 Nucl. Phys. A 799 1] within the error margins, and the uncertainties are smaller. However, significant discrepancies are observed between the theoretical model calculations and the experimental data, which may be attributed to the lack of experimental information about the high-excitation-energy levels in the ⁵²Cr level scheme. This study not only fills a gap in the measurement of the ⁵²Cr inelastic scattering cross-section but also provides important nuclear data for designing and optimizing the next-generation reactors.