MgB₂ superconducting film, as the alloy superconductor with the highest superconducting transition temperature so far, has a broad application prospect in the field of electronics because of its simple structure, long coherent length, no weak connection between grain boundaries, high upper critical field, short electron-phonon scattering time and so on. Raman spectroscopy is an effective method to study the electron-phonon interaction and superconducting band. Moreover, Raman spectroscopy has been used to study the electron-phonon characteristics and superconducting band structure of MgB₂. Research shows that sample quality, grain size and test conditions greatly influence the peak position and shape of the Raman peak of MgB₂. The change of Raman spectrum with temperature is also a research priority. However, the temperature range of MgB₂ variable temperature Raman spectrum is relatively small, which is limited to 83 K to room temperature or the region near the transition temperature. In this work, the Raman spectra of MgB₂ film in a large temperature range are studied. The polycrystalline MgB₂ film was prepared on (0001) SiC substrate via hybrid physical-chemical vapor deposition with grain size ~300 nm and superconducting transition temperature 39.3 K. The Raman spectra of MgB₂, from 20 to 1 200 cm^-1, were measured and studied in the temperature region from 10 to 293 K. The Raman spectra show that Raman peaks related to MgB₂ appear at ~620 cm^-1 in high-frequency region and at ~80 and ~110 cm^-1 in low-frequency region. The frequency of the two Raman peaks in the low-frequency region corresponds to the width of the superconducting energy gap, indicating the dual-gap characteristics of MgB₂. Considering the Raman activity of the four phonon modes in MgB₂, the Raman peak at ~620 cm^-1 in high-frequency region is contributed by the E_2g vibration mode. And as temperature decreases, no obvious peak position shift is observed. Nevertheless, the FWHM of the Raman peak decreases with temperature. Furthermore, the FWHM is 380.7 cm^-1 at 293 K, and 155.7 cm^-1 at 10 K. Analysis shows that the non-harmonic effect caused by the nonlinear coupling between E_2g phonon and electronic system may be the main reason for the linear decrease of the FWHM.