Nowadays, the dusty plasma has become an interesting new branch of the plasma physics. As we all know, the dusty plasmas play a significant role in the space, astrophysical and laboratory environments plasma. But in these days, the studying of the nonlinear waves in dusty plasma have been attracted researchers’ attention to explain many basic phenomena in the plasma physics. The nonlinear waves play an important role in the study of dusty plasmas environments, such as the aster-oid zones, the earth’s mesosphere, the planetary rings etc. In this paper, the propagating characteristics of nonlinear dust acoustic solitary waves in a multicomponent dusty plasma which composed of positively charged dust particles, streaming protons and electrons, Kappa distributed electrons and ions have been studied in detail. The Sagdeev potential method has been employed to research the large amplitude dust acoustic waves. It has an evidence for the existence of compressive and rarefractive solitary waves. With the help of the Sagdeev potential method, the Sagdeev potential function and the bifurcation analysis of phase-portrait have been obtained. Firstly, the Sagdeev potential function have been obtained by the Sagdeev potential method. Then, the variations of phase diagram with different parameters in a two-dimensional autonomous system in the multicomponent dusty plasma system have been investigated. It is found that the system has the linear wave solutions, nonlinear wave solutions and solitary wave solutions at the same time. Meanwhile, the existence of different wave behaviors is closely related to various system factors. Moreover, it is found that only the rarefractive solitary waves exist in the multicomponent dusty plasma system by using the numerical simulation technique. Finally, the important influence of system parameter on the phase diagram, the Sagdeev potential function and the propagating characteristics of nonlinear dust acoustic solitary waves has been discussed clearly. The results have showed that the different system parameters such as Mach number <em>M</em>, the masses, the temperatures, the number densities, the charge numbers of multiple particles and the Kappa distribution parameters for ions and electrons have important effects on the amplitude, the width and the waveform of nonlinear dust acoustic solitary waves.