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Dispersion is one of the important characteristics of dusty plasma. In this paper, the real and imaginary parts of the complex refractive index of dusty plasma are first deduced and verified by the Kramers–Kronig dispersion relation. And then, the dependence of dispersion ability on the temperature, pressure, angular frequency of incident electromagnetic wave, as well as the number density, radius, and charge of dust particles is given. Finally, the theoretical results indicate that: 1) the dispersion ability decreases with the increase of angular frequency; 2) the dispersion ability monotonically varies with the pressure approximately, but nonmonotonically varies with the temperature; and 3) the dispersion ability monotonically increases with the increase of dust particle’s charge, but nonmonotonically changes with the number density and radius of dust particles. In particular, the involved physical explanations are proposed. [ABSTRACT FROM AUTHOR]