The crystals with high quality and perfect property are more and more required following the progress of the information and biological technologies. Under the gravity field on earth, we have the natural convection, which greatly influences the transport process of both the heat and the solute as well as the crystal/solution boundary characteristics, and therefore, the crystal quality and property. The space microgravity environment provides an ideal condition for a pure diffusion crystal growth, to grow perfect single crystals. The space crystal growth was extensively studied with the microgravity experiments over the three decade in satellite, spaceship, space laboratory and space station. This paper summarizes the progresses related with several leading crystals, such as semiconductor, special function crystal, non-linear optical crystal, protein crystal and galley salt crystal.