A Monte Carlo simulation of the terrestrial hydrogen exosphere is used to derive a global model of the exospheric hydrogen density. A third-order spherical harmonic expansion in longitude and colatitude is used to represent H at a particular radius. The h_exos.dat file provides the harmonic expansion coefficients for 40 radii (between 6640 km and 62126 km) for solstice and equinox conditions, and for four levels of solar activity (F10.7 = 80, 130, 180, 230). Details of the Monte Carlo simulation are explained in Hodges (1994). The simulation results show significant differences with previous exosphere models, as well as with the H distributions of the MSIS-86 thermosphere model.