We present an empirical model of the inner magnetosphere, based on proton measurements performed by the charge-energy-mass instrument in the energy range 1--300 keV and in the L range 3--9 during 3 years of the Active Magnetospheric Particle Tracer Explorers/CCE mission (1985 to 1987, i.e., near solar minimum). We have fitted the average proton fluxes at low geomagnetic activity (AE<100 nT) and obtained a multi parametric function, which is the sum of five different parts and depends on energy, L shell, magnetic local time, and a few independent factors. The model is able to accurately reproduce the average perpendicular proton fluxes in the equatorial inner magnetosphere. The various segments of the model function reproduce the effects of physical processes, such as diffusion, on magnetospheric plasma. We describe the methodology followed for the development of the model. Empirical models like this one are critical in our effort to exploit global neutral atom imaging measurements of ongoing and future missions. Furthermore, they serve as a benchmark of theoretical models and numerical simulations of the inner magnetosphere. ¿ 2001 American Geophysical Union