The existence of the Godel rotation parameter in Godel universe creates many interesting special features for Godel-type black holes. In this Letter, motivated by the fact that these new features provide additional tests as to the robustness of the covariant anomaly cancellation method and the effective action technique, we attempt to adopt the analyses to study Hawking radiation from Kerr-Godel black hole. The result is interesting and showing that the covariant anomaly cancellation method and the effective action technique applied to Kerr-Godel black hole yield Hawking temperatures consisten...