This　paper　proposes　a　new　cooperative　projection　neural　network　(CPNN),　which　combines　automatically　three　individual　neural　network　models　with　a　common　projection　term.　As　a　special　case,　the　proposed　CPNN　can　include　three　recent　recurrent　neural　networks　for　solving　monotone　variational　inequality　problems　with　limit　or　linear　constraints,　respectively.　Under　the　monotonicity　condition　of　the　corresponding　Lagrangian　mapping,　the　proposed　CPNN　is　theoretically　guaranteed　to　solve　monotone　variational　inequality　problems　and　a　class　of　nonmonotone　variational　inequality　problems　with　linear　and　nonlinear　constraints.　Unlike　the　extended　projection　neural　network,　the　proposed　CPNN　has　no　limitation　on　the　initial　point　for　global　convergence.　Compared　with　other　related　cooperative　neural　networks　and　numerical　optimization　algorithms,　the　proposed　CPNN　has　a　low　computational　complexity　and　requires　weak　convergence　conditions.　An　application　in　real-time　grasping　force　optimization　and　examples　demonstrate　good　performance　of　the　proposed　CPNN.