This　paper　presents　a　new　cooperative　projection　neural　network　for　fast　solving　quadratic　convex　programming　problems,　including　linear　reconstruction　problems.　The　proposed　cooperative　projection　neural　network　consists　of　a　weighted　combination　of　two　projection　terms.　Compared　with　conventional　projection　neural　networks　and　numerical　optimization　methods,　the　proposed　cooperative　projection　neural　network　has　a　small　model　size　and　no　limit　condition　of　initial　points.　Numerical　results　demonstrate　that　the　proposed　cooperative　projection　neural　network　has　a　faster　speed　than　the　existing　projection　neural　networks.　Therefore,　the　proposed　cooperative　projection　neural　network　can　fast　solve　linear　reconstruction　problems.