We propose and analyze a BPX-type preconditioner for the integral fractional Laplacian on bounded domains. For either quasi-uniform grids or bisection grids, we show that the condition number of the resulting systems remains uniformly bounded with respect to both the number of levels and the fractional power. This is a joint work with Prof. Juan Pablo Borthagaray (UDELAR), Prof. Ricardo H. Nochetto (UMD), and Prof. Jinchao Xu (PSU).