Using classical ensemble method, we investigate the laser ellipticity dependence of double ionization (DI) of H2 molecules. The results show that DI mechanism of H2 molecules depends strongly on laser polarization. As the ellipticity increases, the DI mechanism changes from nonsequential DI to sequential DI. For sequential DI in the case of large ellipticity, the momentum distribution of the two electrons depends sensitively on ellipticity, which indicates the sensitive dependence of the release time of two electrons on ellipticity.