The behavior of linear and nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma including inertialess electrons and positrons, ions, and mobile positive/negative dust grains are studied. Reductive perturbation method is employed for small and finite amplitude DAWs. To investigate the solitary waves, the Korteweg–de Vries (KdV) equation is derived and the solution is presented. By numerical analysis, it is found that the soliton structure of the dust acoustic wave depends upon plasma parameters like electron to ion Fermi temperature ratio, s, dust to ion temperature ratio d and quantum diffraction parameter H.