We extend to study Hawking radiation via tunneling in conformal gravity. We adopt Parikh-Wilczek's semi-classical tunneling method and the method of complex-path integral to investigate Hawking radiation from new rotating AdS black holes in conformal gravity. In this paper, the research on Hawking radiation from the rotating black holes is done in a general system, not limited in dragging coordinate systems any longer. Moreover, there existed some shortcomings in the previous derivation of geodesic equations. Different from the massless case, they used a different approach to derive the geodesic equation of the massive particles. Even the treatment was inconsistent with the variation principle of action. To remedy the shortcoming, we improve treatment to deduce the geodesic equations of massive and massless particles in a unified and self-consistent way. In addition, we also recover the Hawking temperature resorting to the complex-path integral method.