Variational　inequalities　with　linear　inequality　constraints　are　widely　used　in　constrained　optimization　and　engineering　problems.　By　extending　a　new　recurrent　neural　network　[14],　this　paper　presents　a　recurrent　neural　network　for　solving　variational　inequalities　with　general　linear　constraints　in　real　time.　The　proposed　neural　network　has　onelayer　projection　structure　and　is　amenable　to　parallel　implementation.　As　a　special　case,　the　proposed　neural　network　can　include　two　existing　recurrent　neural　networks　for　solving　convex　optimization　problems　and　monotone　variational　inequality　problems　with　box　constraints,　respectively.　The　proposed　neural　network　is　stable　in　the　sense　of　Lyapunov　and　globally　convergent　to　the　solution　under　a　monotone　condition　of　the　nonlinear　mapping　without　the　Lipschitz　condition.　Illustrative　examples　show　that　the　proposed　neural　network　is　effective　for　solving　this　class　of　variational　inequality　problems.　©　Springer-Verlag　Berlin　Heidelberg　2007.