In　this　paper,　we　consider　a　delayed　food-limited　model　with　feedback　control.　By　regarding　the　delay　as　the　bifurcation　parameter　and　analyzing　the　corresponding　characteristic　equations,　the　linear　stability　of　the　system　is　discussed,　and　Hopf　bifurcations　are　demonstrated.　By　the　normal　form　and　the　center　manifold　theory,　the　explicit　formulae　are　derived　to　determine　the　stability,　direction　and　other　properties　of　bifurcating　periodic　solutions.　Finally,　some　examples　are　presented　to　verify　our　main　results.　©　2014　Springer　Science+Business　Media　Dordrecht.