A　Lotka–Volterra　commensal　symbiosis　model　with　density　dependent　birth　rate　that　takes　the　form　dxdt=x(b11b12+b13x−b14−a11x+a12y),dydt=y(b21b22+b23y−b24−a22y),　where　bi　j,　i=　1　,　2　,　j=　1　,　2　,　3　,　4　,　a11,　a12,　and　a22　are　all　positive　constants,　is　proposed　and　studied　in　this　paper.　The　system　may　admit　four　nonnegative　equilibria.　By　constructing　some　suitable　Lyapunov　functions,　we　show　that　under　some　suitable　assumptions,　all　of　the　four　equilibria　may　be　globally　asymptotically　stable,　such　a　property　is　quite　different　to　the　traditional　Lotka–Volterra　commensalism　model.　With　introduction　of　the　density　dependent　birth　rate,　the　dynamic　behaviors　of　the　commensalism　model　become　complicated.　©　2018,　The　Author(s).