The　constrained　L-1　estimation　is　an　attractive　alternative　to　both　the　unconstrained　L1　estimation　and　the　least　square　estimation.　In　this　letter,　we　propose　a　cooperative　recurrent　neural　network　(CRNN)　for　solving　L-1　estimation　problems　with　general　linear　constraints.　The　proposed　CRNN　model　combines　four　individual　neural　network　models　automatically　and　is　suitable　for　parallel　implementation.　As　a　special　case,　the　proposed　CRNN　includes　two　existing　neural　networks　for　solving　unconstrained　and　constrained　L-1　estimation　problems,　respectively.　Unlike　existing　neural　networks　with　penalty　parameters,　for　solving　the　constrained　L-1　estimation　problem,　the　proposed　CRNN　is　guaranteed　to　converge　globally　to　the　exact　optimal　solution　without　any　additional　condition.　Compared　with　conventional　numerical　algorithms,　the　proposed　CRNN　has　a　low　computational　complexity　and　can　deal　with　the　L-1　estimation　problem　with　degeneracy.　Several　applied　examples　show　that　the　proposed　CRNN　can　obtain　more　accurate　estimates　than　several　existing　algorithms.