Relativistic jets in radio galaxies are the most promising candidates for observed ultra-high energy cosmic rays (UHECRs). We examine the radio-galaxy origin of UHECRs through relativistic hydrodynamic simulations of FR I/II type jets and Monte Carlo simulations of particle transport and acceleration. We find that diffusive shock acceleration is the dominant process for E<~10^{18} eV, whereas relativistic shear acceleration at the interface between the jet flow and the cocoon is more important for E>~10^{18} eV. Turbulence acceleration plays a minor role. The resulting energy spectrum may be modeled by a double-power law; the highest energy part of the spectrum is governed by the confinement of elongated cocoons. We then simulate the propagation of UHECRs from cosmological populations of radio galaxies to the Earth through the intergalactic space. Assuming that a fraction of UHECRs originate from several nearby sources and the rest come from cosmological populations, we assess whether the observed energy spectrum and composition in Auger and TA could be explained. The results of the study will be presented.