Major Advisor: AlemuGeleta(PhD) Co-Advisor: Geremew Kenassa (PhD) Abstract Predation is an ecological interaction that can occur simultaneously in any system of species. In this thesis, a prey-predator system is considered. Predators are assumed to consume prey populations, while preys are a source of food for predator’s populations. Thus, a mathematical model is developed to describing the population dynamics of preypredator system using nonlinear first order ordinary differential equations. The model consists of prey population and predator population. The mathematical and stability analysis of the predator-prey model is analyzed. Positivity and boundedness of the model is verified. Free equilibrium is found and shown that it is locally and asymptotically stable. Interior equilibrium is also identified and shown that it is locally, asymptotically and globally stable. Simulation study is conducted to verify the results of mathematical analysis. Lastly, conclusions of the results are forwarded. Key Words: Prey, Predator, Equilibrium points, Stability, Analysis, Population