  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 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 while the inflaton is non-minimally coupled to the gravity and we
find that these non-minimal inflations could be eternal in some parameter
regions.
