Abstract: The principal objective is to discuss the stability and bifurcations of the neutral logistic equation.Some sufficient conditions for the local asymptotical stability of the equilibrium have been provided by employing Jury criterion.Further,the existences of Flip and N-S bifurcations are discussed by using center manifold theorem and bifurcation theory,and we briefly address the necessary and sufficient conditions for the existence of F-N-S bifurcation.By fitting the population data set of Chinese population from 1981 to 2010 we determine the parameter values,which allows us to evaluate the proposed model and discuss the control strategy for controlling the population in China.