Using the reductive perturbation technique, Burgers’ equation is derived for studying the behavior of dust acoustic (DA) shock waves in an unmagnetized dusty plasma, whose constituents are kappa-distributed (superthermal) electrons, Boltzmann distributed ions and positively and negatively charged dust particles. The solution of Burgers’ equation is numerically analyzed. The effects of spectral index κ on the properties of DA shock waves is discussed. It is found that the spectral index κ changes the amplitude of the DA shock waves significantly. The present investigation may be helpful in the understanding of the nonlinear propagation of waves in the pulsar magnetosphere.