Can the simplest two-field model of open inflation survive?

We investigate the quantum fluctuations of an inflaton field in a two-field model of one-bubble open inflation. One of the inflatons is assumed to be responsible for the first false vacuum stage of inflation and the other is assumed to be responsible for the second slow-roll stage of inflation. The mass of the second inflaton is assumed to be negligible throughout the whole era of inflation. We find the supercurvature fluctuations are enhanced by the factor given by the ratio of the Hubble constants at false vacuum and true vacuum. This gives a strong constraint on a class of open inflation models. In particular, this implies the simplest two-field model proposed by Linde and Mezhlumian is in trouble.