We prove the global existence of smooth solutions to the Cauchy problem of Fokker-Planck-Boltzmann equation near Maxwellians for the whole range of cutoff soft potentials. Our results does not rely on the smallness assumption of the parameter in front of the Fokker-Plank operator as in [Xiong-Wang-Wang, KRM,2014]. Our analysis heavily rely on the refined weight-coercivity of the Fokker-Plank operator and the refined weighted energy method.