Core-level binding energies (CLBEs) contain important information about the electronic structure, elemental chemistry, and chemical environment of molecules and materials. Theoretical study of CLBEs can provide insights for analyzing and interpreting the experimental results obtained from X-ray photoelectron spectroscopy, in which overlapping of signals is very common. However, predicting CLBEs from orbital energies of commonly used density functional approximations (DFAs) is challenging, especially when degenerate core-level states exist. The mean absolute errors (MAEs) of absolute CLBEs from DFAs are >
15 eV. The large error is due to the delocalization error, which can be reduced by localized orbital scaling correction (LOSC) methods. In this work, we develop a new method, namely, the linear response LOSC (lrLOSC), for predicting CLBEs from ground-state density functional calculations by both employing localized orbitals and describing the screening effect within the LOSC scheme. Numerical results show that utilizing localized orbitals in lrLOSC is important for the calculation of CLBEs using the LOSC methods when degenerate or nearly degenerate core-level orbitals exist. Furthermore, capturing the screening effect can universally improve the prediction of both absolute CLBEs and relative CLBEs that are closely related to the chemical shifts in X-ray photoelectron spectroscopy. With the new method, the MAEs of absolute CLBEs are reduced to around 3 eV and the MAEs of relative CLBEs are reduced to around 0.16 eV.