In　this　paper,　we　propose　Bernstein　polynomial　estimation　for　the　partially　linear　model　when　the　nonparametric　component　is　subject　to　convex　(or　concave)　constraint.　We　employ　a　nested　sequence　of　Bernstein　polynomials　to　approximate　the　convex　(or　concave)　nonparametric　function.　Bernstein　polynomial　estimation　can　be　obtained　as　a　solution　of　a　constrained　least　squares　method　and　hence　we　use　a　quadratic　programming　algorithm　to　compute　efficiently　the　estimator.　We　show　that　the　estimator　of　the　parametric　part　is　asymptotically　normal.　The　rate　of　convergence　of　the　nonparametric　function　estimator　is　established　under　very　mild　conditions.　The　small　sample　properties　of　our　estimation　are　provided　via　simulation　study　and　compared　with　regression　splines　method.　A　real　data　analysis　is　conducted　to　illustrate　the　application　of　the　proposed　method.　(C)　2014　The　Korean　Statistical　Society.　Published　by　Elsevier　B.V.　All　rights　reserved.