Electron-ion collision is one of the fundamental processes in atomic and molecular physics, and the study of this process can provide insight into the mechanism of electron-atom/ion interaction. It has important applications in plasma physics and astrophysics. Accurate electron-impact cross-sections are important in plasma modeling. In generally, total EISI cross-sections consists of the direct ionization (DI) and the indirect ionization processes, with the latter further divided into excitation autoionization (EA), resonant excitation double auto-ionization (REDA) and resonant excitation auto- double ionization (READI) processes. In this work, the electron-impact single ionization (EISI) crosssections for the ground state Kr4d¹⁰5s²4f¹³ of W¹³⁺ ions are calculated in detail by using the level-to-level distorted-wave (LLDW) method, which mainly includes the contributions of direct ionization (DI) and excited auto-ionization (EA) cross-sections to the EISI cross-sections. Our computational results demonstrate that when configuration interaction are incorporated, the calculated values show excellent agreement with experimental data for electron impact energies exceeding 500 eV. However, significant discrepancies persist near the ionization threshold. we have confirmed that these discrepancies primarily originate from the presence of long-lived metastable ions. To achieve better agreement with experimental observations, we further calculated EISI cross-sections for 71 energy levels of the metastable state 4 d¹⁰ 5 s² 4 f¹² 5p with lifetimes greater than 1.5×10^-5s. The total EISI cross-sections of these 71 energy levels were obtained by theoretical fitting and compared with the experimental results by Schury et al. (Figure), and it was found that our results were in good agreement with the experimental results of Schury et al. after considering the contribution of long-lived metastable.