A free-piston hydrogen fueled engine is considered as one of the next power systems which is able to obtain high efficiency and low emission, simultaneously. In this study, in order to ensure the possibility as the next generation power system, the combustion characteristics and the performance of the free-piston hydrogen fueled engine are analyzed by using the linear RICEM for the change of injection pressure and equivalence ratio. As the results, in-cylinder maximum pressure is shown at injection pressure $P_{inj}$=6bar. Backfire phenomenon is not observed under experimental condition and knock occurs over ${Phi}=0.8$. The thermal efficiency is the highest at injection pressure, $P_{inj}$=6bar and equivalence ratio, ${Phi}=0.7$, respectively.