The accurate photoneutron cross section of the \(^{27}\) Al nucleus has a significant impact on resolving differences in existing experimental data and enhancing the precision of nuclear reaction rate calculations for \(^{26}\) Al in nuclear astrophysics. The photoneutron cross sections for the \(^{27}\) Al( \(\gamma\) , n) \(^{26}\) Al reaction, within the neutron separation energy range of 13.2 \(-\) 21.7 MeV, were meticulously measured using a new flat efficiency detector array at the Shanghai Laser-Electron Gamma Source. The uncertainty of the data was controlled to below 4% throughout the process, and inconsistencies between the present data and existing data from different gamma sources, as well as the TENDL-2021 data, are discussed in detail. These discussions provide a valuable reference for addressing discrepancies in the \(^{27}\) Al( \(\gamma\) , n) \(^{26}\) Al cross-section data and improving related theoretical calculations.