We performed grand canonical Monte Carlo simulations for a Lennard-Jones fluid confined in a jungle-gym (JG) nanospace of cubic structure modeled on a specific type of metal organic frameworks (MOFs) to investigate freezing phenomena. Our simulations clarified that the JG nanospace with the pore sizes from 5 sigma to 11 sigma strongly depresses freezing due to a geometrical hindrance effect, resulting in far lower freezing temperature than the bulk freezing point. The fluid-rod interaction is found to give little effect on the freezing temperature in the larger pore sizes. For smaller pores from 2 sigma to 3 sigma, on the other hand, a dominant factor is a template effect to enhance the localization of molecules into a specific configuration that matches the locations of potential minima, leading to a variety of molecular configurations. In this range of smaller pore sizes, the solidification temperatures are higher than those of the larger pores mainly due to strong influence of the fluid-rod interaction but are still lower than the bulk freezing temperature. In addition, a unique solid-to-solid transition is observed in a specific size of pore of 2.73 sigma, which is caused by structural correlation between adjacent cells. On the basis of these results, a phase diagram in the JG nanospace is drawn.