The thermal conductivity (κ) of glasses is known to always be lower than that of their corresponding crystals due to the stronger phonon-phonon scattering in the former. However, it is unknown whether this relation holds for metal-organic frameworks. Here, we report our discovery of an inverse relation in κ between glass and crystal for two zeolitic imidazolate frameworks (ZIFs), ZIF-4 and ZIF-62, that is, melt-quenched ZIF-4 and ZIF-62 glasses possess higher thermal conductivities than their crystalline counterparts. We find that the ZIF crystal pellets exhibit ultralow κ (∼0.1 W m-1 K-1) and that the higher κ of the ZIF glasses is due to the collapse of internal cavities and higher atomic number density in the latter. For other systems like oxides, vitrification causes higher free volume, but the opposite is found for the ZIFs, that is, lower free volume owing to the partial collapse of the crystalline framework upon melting.