Abstract: Differential mosquito model with piecewise constant arguments and stage-structured is modeled.Firstly the discrete solutions of the model is achieved to obtain the local and bifurcation behaviors.Thus,the sufficient conditions for the local asymptotic stability about the zero and positive equilibrium are derived by using the linear stability theorem.Secondly it is shown that the mosquito model can undergo Saddle-Node bifurcation and Flip bifurcation nearby equilibrium when the bifurcation parameter exceeds a critical value.Furthermore,the formulas distinguishing the stability of bifurcation solutions are constructed by using the normal form;center manifold theorem and bifurcation theory.Finally numerical simulations are given to show the effectiveness of the theoretical analysis and exhibit the complex dynamic behavior.