In this research, theoretical method was used to examine the excitation and depression state for two-stream Buneman’s instability (BI) when we assumed an inhomogeneous, anisotropic, multi ions species with the presence of dust grains in plasma. The plasma also studied at different temperatures state. The diffusion equation was also derived and solved in one dimension for the Buneman’s instabilities that arise in such a situation within plasma. We develop the single-ion theory into a multiple-ion-species theory. This study concluded that: degree of plasma inhomogeneity, electron to ions temperature ratio, multi ions species and dust grains which have thermal velocity play a very important role in the depression and excitation of instability such Buneman’s instability.