The kinetic process of liquid-liquid phase separation in the undercooled Ni-20at%Pb hypermonotectic alloy melts was analyzed theoretically. The results showed that liquid-liquid separation could not be inhibited due to smaller nucleation barrier and bigger nucleation rate of Pb-rich droplets. In the course of liquid-liquid phase separation, the volume fraction of Pb-rich droplets was thought as a function of time or temperature. At a certain cooling rate, the volume fraction was mainly controlled by the undercooling of Ni-Pb hypermonotectic melts. Based on the above results, a homogeneous solidification criterion for the undercooled Ni-20at%Pb hypermonotectic alloy melts was developed. Such a criterion predicted that the homogeneous microstructure could be obtained at the undercooling 263K, and the experimental results accorded with the predicting ones on the whole.