Realization of the Bose-Einstein condensation (BEC) of positronium is a long-standing challenge of positron physics. Since the positron is the antimatter of the electron, the positronium is the antimatter of itself, and its gravity interaction is a sum of matter and antimatter components. In this sense, it can be used to study antimatter gravity. It can also be used as a source of a γ-ray laser. We have proposed a new method to realize a positronium BEC: a combination of thermalization in a cold silica target and laser cooling using 1S-2P transitions. We have started some basic studies based on our new idea. Here we report a preliminary result of our positronium thermalization measurement in cryogenic environment and development status of a new laser system for positronium cooling.