In this study a mathematical model of two competing predators sharing one prey in homogeneous environment, with Holling type-I functional responses, was introduced. The model was formed by considering logistic law for both prey and predator where prey abundance was used to determine carrying capacity of predators. Stability of the equilibrium points of the system was then studied. The conditions for the persistency which were interpreted as efficiency of search and capture, were then obtained. Numerical simulations showed that the coexistence and extinction of the predators depend on how close the efficiency of searching and capture of the two predators.