In　this　paper,　consensus　analysis　and　design　are　investigated　for　discrete-time　multi-agent　systems　(MASs)　with　consecutive　packet　losses　in　communication　links　of　directed　communication　topology.　It　is　assumed　that　at　each　transmitted　instant,　the　packet　loss　is　stochastic　and　described　by　Bernoulli　distribution,　but　during　a　given　time　window,　the　data　could　be　successfully　transmitted　to　the　agent　from　each　of　its　neighbors.　First,　we　utilize　the　incidence　matrix　of　a　directed　spanning　tree　of　the　communication　topology　to　construct　a　linear　transformation　matrix　so　that　the　consensus　problem　is　equivalently　transformed　into　a　mean　square　asymptotic　stability　problem　of　a　reduced-order　system.　Second,　by　using　Lyapunov-Krasovskii　functional　approach,　we　derive　some　sufficient　conditions　of　consensus　criterion　in　terms　of　linear　matrix　inequalities　(LMIs).　These　conditions　express　the　relationship　among　the　control　gain　matrix,　packet　loss　rate,　and　the　number　of　consecutive　packet　losses.　Based　on　the　conditions,　gain　matrix　in　the　consensus　protocol　is　designed　to　guarantee　the　MAS　with　stochastic　packet　losses　to　achieve　mean　square　asymptotic　consensus.　Moreover,　for　the　special　case　of　undirected　communication　topology,　by　using　the　matrix　decomposition　method,　the　variables　of　LMIs　are　transformed　into　the　low-order　conditions　independent　of　the　network　size.　Finally,　some　numerical　examples　are　given　to　show　the　effectiveness　of　the　proposed　method.