The microstructures of Mo-Nb alloy single crystals grown by electron beam floating zone melting were studied using the optical metallograph (OM), scanning electron microscopy (SEM), electron back scatter diffraction (EBSD) and transmission electron microscopy (TEM). The results show that molybdenum-niobium alloy single crystals consist of a mass of sub-grain microstructure. With the increasing of the growth rate of the single crystals, the size of the sub-grain decreases and the growth striations appear at the same time. But the degree of segregation of the alloying element niobium increases with increasing of the growth rate. The increasing content of alloying element Nb also decreases the size of the sub-grain. The size of the sub-grains changes after high temperature annealing process in vacuum.