Traditional　biological　neural　networks　cannot　simulate　the　real　situation　of　the　abrupt　synaptic　connections　between　neurons　while　modeling　associative　memory　of　human　brains.　In　this　paper,　the　memristive　multidirectional　associative　memory　neural　networks　(MAMNNs)　with　mixed　time-varying　delays　are　investigated　in　the　sense　of　Filippov　solution.　First,　three　steps　are　given　to　prove　the　existence　of　the　almost　periodic　solution.　Two　new　lemmas　are　proposed　to　prove　the　boundness　of　the　solution　and　the　asymptotical　almost　periodicity　of　the　solution　by　constructing　Lyapunov　function.　Second,　the　uniqueness　and　global　exponential　stability　of　the　almost　periodic　solution　of　memristive　MAMNNs　are　investigated　by　a　new　Lyapunov　function.　The　sufficient　conditions　guaranteeing　the　properties　of　almost　periodic　solution　are　derived　based　on　the　relevant　definitions,　Halanay　inequality　and　Lyapunov　function.　The　investigation　is　an　extension　of　the　research　on　the　periodic　solution　and　almost　periodic　solution　of　bidirectional　associative　memory　neural　networks.　Finally,　numerical　examples　with　simulations　are　presented　to　show　the　validity　of　the　main　results.