We succeeded in the in situ observation of liquid-liquid phase separation of glass under microgravity at the Japan Microgravity Center (JAMIC), which provides a 10 s microgravity duration. The microgravity level is 10^-5 g (g≡gravitational field at Earth's surface). We constructed an apparatus for the observation of phase separation suitable for the experimental facility. The melt of 3BaO•97B₂O₃ (mol%) was held as a film on a Pt wire loop. The sample was initially heated above the immiscibility temperature and held at that temperature. After the homogenization stage, the melt was cooled. Liquid-liquid phase separation of the melt was observed directly with a video camera. It was found that the nucleation and growth of phase-separated particle under microgravity are slower than in the case of 1-g, and the delay time of phase separation between the case of microgravity and 1-g depends on the flow rate of the melt under microgravity. These observations could be interpreted in terms of Marangoni convection and a change of diffusion.