In the paper [Wu D et al. Sci. sin. G: Phys. Mech. Astron. 43 115], starting from the action of a massive particle's Lagrangian, we have made a new, unified derivation of the timelike and null geodesics of a rotating Kerr black hole. Our results demonstrate that one need not constrain himself to adopt the dragging coordinate system to investigate the tunneling radiation of rotating black holes. That work completely overcomes all shortcomings existing in the previous related researches, thus making Parikh-Wilczek's semi-classical approach more perfect and consistent. In this paper, we extend that work to the case of a rotating charged black hole to present a new derivation of the geodesic equation of a massive charged particle in the Kerr-Newman black hole and to reinvestigate its tunneling radiation.