The hydrodynamic-fluid model and the self-consistent dust charging model are used to investigate the Bohm criterion for the dusty plasma sheath. The variation of the ion critical Mach number and the dust Mach number with dust density are presented, and the relation between the dust surface potential and the dust density at the sheath edge is discussed. It is shown that the ion velocity entering the sheath would exceed the ion sound velocity due to the existence of dust particles. The ion critical Mach number began declining after a maximum with the incessant increase of the dust density. The numerical results satisfy the qualitative analysis of the Sagdeev potential.