Droplets of Ni-50%Cu alloy with different sizes are rapidly solidified under the condition of microgravity and containerless state within a 3m drop tube. With the increase of undercooling, the microstructural evolution has shown a transition from coarse dendrites to equiaxed grains. The maximum cooling rate of 8×103K/s and the undercooling up to 218K(014TL) are obtained in experiment. Based on a theoretic analysis, the heterogeneous nucleation occurs preferably in Ni-50%Cu droplets. The nucleation rate exceeds 1012 m-3s-1. The rapid dendritic growth of Ni-50%Cu alloy proceeds from the solutal-diffusion-controlled to the thermal-diffusion-controlled growth with the enhancement of undercooling. Under the undercooling of 68K, the segregation degree of liquid at the growing interface reaches a maximum value.