In recent years, lithium niobate single crystals have attracted much attention due to their excellent physical properties and potential applications in the modern science and technology. However, it is difficult to grow lithium niobate single crystals with a high quality and large size, which can match different kinds of practical needs. Different growthing methods of lithium niobate single crystals and their respective characteristics are presented in this paper. Problems occuring in the growth process of lithium niobate single crystals are also analyzed.