It is well known that multi-component alloys form bulk metallic glasses (BMGs) from the supercooled liquid state without rapid quenching. However, the mechanism of phase selection between crystal and glass states has not been fully clarified. To obtain an insight into the glass-forming processes, we carried out in-situ observation on the solidification of Zr-based BMG-forming alloys from its supercooled liquids by time-resolved X-ray diffraction combined with the conical nozzle levitation (CNL) technique to achieve a containerless melting. For Zr-based alloys, we succeeded in detecting the X-ray diffraction patterns during glass formation from the supercooled liquid state as well as the crystallization from the liquid state. Furthermore we performed the precise structure analysis of supercooled state of Zr-based binary liquids. Based on the liquid structure and in-situ observation results, we discussed about the phase selection mechanism between crystal and glass states.