This　technical　note　develops　a　neural　dynamical　approach　to　nonlinear　programming　(NP)　problems,　whose　equilibrium　points　coincide　with　Karush-Kuhn-Tucker　points　of　the　NP　problem.　A　rigorous　analysis　on　the　global　convergence　and　the　convergence　rate　of　the　proposed　neural　dynamical　approach　is　carried　out　under　the　condition　that　the　associated　Lagrangian　function　is　convex.　Analysis　results　show　that　the　proposed　neural　dynamical　approach　can　solve　general　convex　programming　problems　and　a　class　of　nonconvex　programming　problems.　Two　nonconvex　programming　examples　are　provided　to　demonstrate　the　performance　of　the　developed　neural　dynamical　approach.