A scheme to simulate the multi-phonon quantum Rabi model (QRM) based on trapped ions is proposed in this paper. In this scheme, an ion is simultaneously driven by two laser beams tuned to nonresonant jth-order red and blue sidebands. Under certain conditions, the interaction between the driving lasers and the ion in the system can be described by the multi-phonon resonance QRM. In particular, when the frequency of the simulated two-level system is 3j times that of the simulated bosonic mode, the system exhibits resonant 3j-phonon coupling via intermediate states connected by counter-rotating processes. As a typical example, a three-phonon resonance QRM has been theoretically analyzed, and a nine-phonon state has been generated through adiabatic passage using this model.