In a plasma system, ion–ion instability is excited due to the counter streaming of ion beams. An experiment has been carried out to observe the ion–ion instability in a dusty plasma device and in the presence of Ar as a background gas. The experiment is performed in a double plasma device which is 90 cm in diameter and 120 cm in length, separated by a mesh grid of 81% optical transparency. Glass beads of 4 µm average diameters are used as dust grains for the whole set of experiments and are allowed to fall within a particular region of the plasma column inside the system. The growth and decay rate of the ion–ion instability is observed by shifting a probe spatially away from the grid in the target section with changing dust density in the system. Experiments have been carried out under different dust density conditions. According to our experimental findings, the suppression mechanism can be discussed in terms of the dust density inside the system. The distributions of ions, which are taking part in the formation of the instability, are also observed at the respective dust composition. The instability is found to be suppressed completely at a certain critical value of the dust density (Ndcr).