Solar energetic particles (SEPs) pose a serious radiation hazard to spacecraft and astronauts. The highest energy SEPs are a significant threat even in heavily shielded applications. We present a new probabilistic model of very high energy differential peak proton fluxes. The model is based on GOES/HEPAD observations between 1986 and 2018, i.e., covering very nearly three complete solar cycles. The SEP event list for the model was defined using a statistical criterion derived by setting the possibility of false detection of an event to 1%. The peak flux distributions were calculated for the interpolated energies 405 MeV, 500 MeV and 620 MeV, and modelled with exponentially cut off power law functions. The HEPAD data were cleaned and corrected using a “bow-tie” method which is based on the response functions of the HEPAD channels P8–P10 found in the instrument calibration reports. The results of the model are available to the Space Weather community as a web-based tool at the ESA’s Space Situational Awareness Programme Space Weather Service Network.