In this study, we proposed a deterministic mathematical model that attempts to explain the propagation of a rumor using epidemiological models approach. The population is divided into four classes which consist of ignorant individuals, I(t), spreaders targeting community through media, M(t), spreaders targeting community through verbal communication, G(t) and stiflers, R(t). We explored existence of the equilibria and analyzed its stability. It was established that rumour-free equilibrium E0 is locally asymptotically stable if R0 1 leads to new rumor spreading in the population. Numerical simulations of the dynamic model are carried out on the system to confirm the analytical results. We see that the dynamics of rumor spreading show similar behavior to that found in the dynamics of infectious diseases except that the spread depends on the classes of spreader.