In the undercooled melt of $Pd_{40}Cu_{30}Ni_{10}P_{20}$ alloy, the solidification behavior including nucleation and growth of crystals at the micrometer level has been observed in-situ by use of a confocal scanning laser microscope combined with an infrared image furnace. The $Pd_{40}Cu_{30}Ni_{10}P_{20}$ alloy specimens were cooled from the liquid state to glass transition temperature. 575 K, at various cooling late under a helium gas flow. According to the cooling rate, the morphologies of the solidification front are changed among various types, irregular jog like front, columnar dendritic front, cellular grain, star like shape jog and fine grain, etc. The velocities of the solid-liquid interface are measured to be $10^{-5}{sim}10^{-8}$ m/s which are at least two orders higher than the theoretical crystal growth rates. Combining the morphologies observed in terms of cooling rates and their solidification behaviors, we conclude that phase separation takes place in the undercooled molten $Pd_{40}Cu_{30}Ni_{10}P_{20}$ alloy. The continuous cooling transformation (CCT) diagram was constructed from solidification onset time at various linear cooling conditions with different rate. The CCT diagram suggests that the critical cooling rate for glassy solidification is about 1.5 K/s, which is in agreement with the previous calorimetric findings.