Based on the magnetohydrodynamics (MHD) theory, the propagating characteristics of (3+1)-dimensional nonlinear dust acoustic waves (DAW) have been studied in an unmagnetized warm dusty plasma containing dust particles, electrons, and ions with nonthermal distribution. Firstly, the dynamic evolution of (3+1)-dimensional nonlinear DAW has been investigated by deriving the dispersion relation via the linearized method, the Kadomtsev–Petviashvili (KP) equation via the reductive perturbation method, and the Sagdeev potential function via the Sagdeev potential technique. Secondly, numerical simulations have been performed to investigate the effects of various system parameters on the nonlinear dispersion relation, the KP equation, phase-space structures, Sagdeev potential profiles, and the dust acoustic solitary waves under the isothermal ( \gamma =1 ) and adiabatic ( \gamma =5/3 ) conditions. Finally, the results indicate that the propagation properties of nonlinear rarefactive dust acoustic solitary waves are influenced by various system parameters. Moreover, the frequency, amplitude, width and waveform of the DAW are affected by nonthermal ions, and particle’s temperature in an unmagnetized warm dusty plasma under both isothermal and adiabatic states.