Modeling of High Purity Germanium (HPGe) detector on a wide energy range is important in gamma-ray spectroscopy. The precisely modeled detector can be used for proton-induced prompt gamma-ray spectroscopy. In this work, we used both the gamma-rays of calibration sources and prompt gamma-rays emitted in proton capture reactions to model a coaxial p-type HPGe detector using Geant4 Monte Carlo simulation for the gamma-ray energy range of 59–10764 keV. The calibration sources were 137Cs, 241Am, 60Co, 152Eu, and 133Ba, while the prompt gamma-rays were due to the gamma-ray cascades following the 27Al(p,γ)28Si reaction capture at the resonant energies of 992, 1317 and 2483 keV, as well as the 23Na(p,γ)24Mg reaction capture at the resonant energies of 1417 and 1395 keV. According to the results obtained, the presented simulated and experimental spectra show a good agreement. In addition, the mean and maximum relative deviations between experimental and simulated efficiencies corresponding to 27 major peaks are smaller than 5% and 15%, respectively.