Multidirectional　associative　memory　neural　networks　(MAMNNs)　are　constructed　to　simulate　the　many-to-many　association,　and　they　are　applied　widely　in　many　fields.　It　is　important　to　explore　the　global　stability　of　the　periodic　solution　of　MAMNNs.　In　this　paper,　MAMNNs　with　discontinuous　activation　functions　and　mixed　time-varying　delays　are　considered.　Firstly,　we　investigate　the　conditions　for　the　existence　of　the　periodic　solution　by　using　the　Mawhin-like　coincidence　theorem,　and　a　special　connecting　weight　matrix　is　constructed　to　prove　the　existence　of　the　periodic　solution.　Secondly,　the　uniqueness　and　global　exponential　stability　of　the　periodic　solution　are　explored　for　the　non-self-connected　system　by　introducing　a　Lipschitz-like　condition.　Finally,　numerical　simulations　are　given　to　illustrate　the　effectiveness　of　our　main　results.