The development of detection techniques and equipment for aircraft surface damage has significant practical significance for flight safety and operational efficiency. Spectral matching technology is a crucial technology that must be addressed in the hyperspectral detection of aircraft surface damage. The recognition accuracy of different spectral matching algorithms often varies depending on the research object. To use a spectral matching algorithm to achieve damage identification of aircraft samples, this article first built an indoor near-infrared hyperspectral system for aircraft surface damage detection and collected hyperspectral data of reference samples and skin samples. It produced standard spectra of two types of pixels using damaged pixel spectra and non-destructive pixel spectra. Subsequently, based on the matching method for calculating the similarity between the measured pixel spectrum and the standard spectrum, four types of single spectrum matching algorithms, namely spectral angle (SA), Mahalanobis distance (MD), spectral information divergence (SID), and spectral correlation coefficient (SCC), and six types of combined spectrum matching algorithms, were used for damage identification of two types of aircraft samples. The accuracy of multiple spectral matching algorithms’ damage identification results was evaluated using the overall classification accuracy P_a and Kappa coefficient. A reasonable threshold group that can better meet the detection requirements is provided by optimizing the threshold parameters of single algorithms, such as SA, MD, SID, and SCC. Furthermore, based on the above four types of single matching algorithms, six types of combined matching algorithms were designed and used for sample damage identification, like SA-MD, SA-SID, SA-SCC, MD-SID, MD-SCC, and SID-SCC. The results show that the identification accuracy of those combined algorithms is relatively higher than that of any matching algorithms. Finally, this article presents the optimal single matching algorithm and combination matching algorithm for damage identification of aircraft samples, with the SCC algorithm and MD-SCC algorithm achieving damage identification rates of over 95% and 97.5% for both types of samples, respectively. This can provide technical support for hyperspectral detection of aircraft surface damage in the outfield.