Nowadays, the dusty plasma has become an interesting new branch of the plasma physics. As is well known, the dusty plasmas play a significant role in the space, astrophysical and laboratory environments. In these days, the studying of the nonlinear waves in dusty plasma has attracted researchers’ attention, in order to explain many basic phenomena in the plasma physics. The nonlinear waves play an important role in studying dusty plasma environments, such as the aster-oid zones, the earth’s mesosphere, and the planetary rings. In this work, the propagating characteristics of nonlinear dust acoustic solitary waves in a multicomponent dusty plasma which is composed of positively charged dust particles, streaming protons and electrons, Kappa distributed electrons and ions are studied in detail. The Sagdeev potential method is employed to investigate 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 are obtained. Firstly, the Sagdeev potential function is 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 are 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 are discussed clearly. The results show that the different system parameters such as Mach number M, 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 amplitudes, the widths and the waveforms of nonlinear dust acoustic solitary waves.