The nonlinear propagation of the dust-acoustic (DA) waves in a dusty plasma consisting of Boltzmann-distributed electrons and ions, and mobile charge fluctuating positive dust has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and is responsible for the formation of the DA shock waves in such a dusty plasma. The basic features of such DA shock waves have been identified. The basic features of the DA shock waves predicted in this investigation should be useful in understanding the properties of localized waves in some space dusty plasmas.