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We study the lattice thermal conductivity of isotope diamond superlattices consisting of 12C and 13C diamond layers at various superlattice periods. It is found that the thermal conductivity of a superlattice is significantly deduced from that of pure diamond because of the reduction of the phonon group velocity near the folded Brillouin zone. The results show that asymmetric superlattices with a different number of layers of 12C and 13C diamonds exhibit higher thermal conductivity than symmetric superlattices even with the same superlattice period, and we find that this can be explained by the trade-off between the effects of phonon specific heat and phonon group velocity. Furthermore, impurities and imperfect superlattice structures are also found to significantly reduce the thermal conductivity, suggesting that these effects can be exploited to control the thermal conductivity over a wide range.