Track-structure Monte Carlo simulations are useful tools to evaluate initial DNA damage induced by irradiation. In the previous study, we have developed a Gean4-DNA-based application to estimate the cell surviving fraction of V79 cells after irradiation, bridging the gap between the initial DNA damage and the DNA rejoining kinetics by means of the two-lesion kinetics (TLK) model. However, since the DNA repair performance depends on cell line, the same model parameters cannot be used for different cell lines. Thus, we extended the Geant4-DNA application with a TLK model for the evaluation of DNA damage repair performance in HSGc-C5 carcinoma cells which are typically used for evaluating proton/carbon radiation treatment effects. For this evaluation, we also performed experimental measurements for cell surviving fractions and DNA rejoining kinetics of the HSGc-C5 cells irradiated by 70 MeV protons at the cyclotron facility at the National Institutes for Quantum and Radiological Science and Technology (QST). Concerning fast-and slow-DNA rejoining, the TLK model parameters were adequately optimized with the simulated initial DNA damage. The optimized DNA rejoining speeds were reasonably agreed with the experimental DNA rejoining speeds. Using the optimized TLK model, the Geant4-DNA simulation is now able to predict cell survival and DNA-rejoining kinetics for HSGc-C5 cells.