A　syrphid　fly-aphid　model　with　stage　structure　for　predator　population　is　considered,　in　which　only　the　immature　predator-natural　enemy　syrphid　fly　can　prey　on　pest-aphid.　By　applying　Lyapunov　functions　and　LaSalles　invariance　principle,　we　show　that　the　global　asymptotic　stability　of　the　interior　equilibrium　for　the　considered　model.　We　also　obtain　results　on　the　existence　and　stability　of　periodic　solutions.　Numerical　simulations　are　also　performed　to　illustrate　the　validity　of　our　results.　©　2017　Journal　of　Nonlinear　Functional　Analysis.