A model for the spectral response function of large volume germanium gamma-ray detectors in the range of incident gamma-ray energies from 60 keV to 6.2 MeV has been developed and applied to a 39% high purity germanium detector. Functional forms for describing the various features of the response function are based either on empirical functions or on analytical expressions of the interaction mechanisms. Improved functions are formulated to give good agreement to the experimental spectra near the Compton edge in the Compton continuum of the primary and annihilation photons. To form the complete detector response function only nine linear and six nonlinear parameters are needed. Validity of the model is demonstrated by comparing the regenerated spectra of 241Am, 51Cr, 137Cs, 54Mn, 28Al, 37S, and 16N and the synthesized spectra of 24Na and 133Ba using the response function to the equivalent experimental spectra.