The logistic growth model with time delay has developed from the classical logistic model, where as in the growth logistic model with time delay, the growth process delay from a population is calculated. This delay cause population decrease then increase so oscillation appears in population growth. So, the solution is not a monotonous function. The result of analysis indicate that the logistic growth model with time delay have two equilibrium points. Each equilibrium points is analyzed for their stability based on time delay variation on the population growth. The longer time delay in the population growth can cause the unstable growth, hence the population decrease and become extinct