In this talk, we study the solutions, which are probability measures with some finite moments, to the non-cutoff homogenous Boltzmann equation. In the Maxwellian molecules case and the moderately soft potentials, the infinite energy solutions are not excluded. Moreover, the smooth effect of the solution is discussed if the initial datum is not a single Dirac mass. This is a joint work with Prof. Tong YANG and Prof. Yoshinori MORIMOTO.