Based on the magnetohydrodynamics (MHD) theory, the propagating characters of (3+1)-dimensional nonlinear dust acoustic waves (DAW) have been studied in an unmagnetized warm dusty plasma which containing with the dust particles, electrons, and nonthermal distributed ions respectively. Firstly, the dynamic evolution of (3+1)-dimensional nonlinear DAW has been invesgated with the dispersion relation, the Kadomtsev–Petviashvili (KP) equation and the Sagdeev potential function by the help of the linearized method, the reductive perturbation method and the Sagdeev potential technique, respectively. Secondly, the numerical simulations have been performed to research the effects of various system parameters on the nonlinear dispersion relation, the KP equation, the phase-space structures, the Sagdeev potential profiles, and the dust acoustic solitary waves for the isothermal (γ=1) and adiabatic (γ=5/3) conditions, respectively. Finally, the results can be concluded that the propagating properties of the nonlinear rarefactive dust acoustic solitary wave can be influenced by the various system parameters. Moreover, the frequency, the amplitude, the width and the waveform of DAW have been effected by the nonthermal ions, the partical’s temperature in an unmagnatized warm dusty plasma under the isothermal and adiabatic states, respectively.