A　kind　of　stage-structured　predator-prey　model　with　Beddington-DeAngelis　functional　response　incorporating　a　prey　refuge　is　investigated　in　this　paper.　By　analyzing　the　corresponding　characteristic　equations,　the　local　stability　of　the　equilibria　is　investigated.　Moreover,　Hopf　bifurcations　occur　at　the　positive　equilibrium　as　the　delay　τ　crosses　some　critical　values.　Further,　the　influence　of　prey　refuge　on　densities　of　predator　species　and　prey　species　is　investigated.　Numerical　simulations　are　carried　out　to　illustrate　our　main　results.　©　2015　Elsevier　Inc.