Is non-minimal inflation eternal?

The possibility that the non-minimal coupling inflation could be eternal is investigated. We calculate the quantum fluctuation of the inflaton in a Hubble time and find that it has the same value as that in the minimal case in the slow-roll limit. Armed with this result, we have studied some concrete non-minimal inflationary models including the chaotic inflation and the natural inflation, in which the inflaton is non-minimally coupled to the gravity. We find that the non-minimal coupling inflation could be eternal in some parameter spaces.