Modern cosmological models include a nearly neutral, non-baryonic form of matter with extremely low speed in the context of structure formation, commonly known as ``cold dark matter''. Astrophysical observations indicate that dark matter constitutes 26.4% of the Universe's critical density and 84.4% of its total matter content. However, the nature of dark matter is still unknown. One of the most promising dark-matter candidates is the neutralino $\chi$, which could annihilate via the process $\chi \bar{\chi} \rightarrow X \gamma$, where $X$ represents either a $\gamma$, $Z$ or $H$ boson. In the approximation of non-relativistic neutralinos, this interaction may lead to monoenergetic gamma-ray emissions, which would represent smoking-gun signatures in the gamma-ray energy spectrum. The main objective of this thesis is the search for spectral lines in the gamma-ray energy flux using eight years of data collected with the space-borne Dark Matter Particle Explorer~(DAMPE). An efficient gamma-ray selection algorithm is developed, using both standard selection criteria and machine learning methods. A precise fitting method within reduced energy windows and a statistical significance evaluation tool are used to search for dark-matter annihilation lines in the gamma-ray energy spectrum. No line signal is detected between 5~GeV and 1~TeV across several regions of interest in the sky. Nevertheless, upper limits at the 95% confidence level are set on the dark-matter annihilation-induced gamma-ray flux. Constraints on the velocity-averaged cross section for neutralino annihilation into two gamma rays are estimated for different dark-matter density profiles.