In　this　paper,　we　introduce　a　class　of　stochastic　neural　networks　with　fractional　Brownian　motion　(fBm)　and　Poisson　jumps.　We　also　concern　mean-square　dissipativity　of　numerical　methods　applied　to　a　class　of　stochastic　neural　networks　with　fBm　and　jumps.　The　conditions　under　which　the　underlying　systems　are　mean-square　dissipative　are　considered.　It　is　shown　that　the　mean-square　dissipativity　is　preserved　by　the　compensated　split-step　backward　Euler　method　and　compensated　backward　Euler　method　without　any　restriction　on　stepsize,　while　the　split-step　backward　Euler　method　and　backward　Euler　method　could　reproduce　mean-square　dissipativity　under　a　stepsize　constraint.　The　results　indicate　that　compensated　numerical　methods　achieve　superiority　over　non-compensated　numerical　methods　in　terms　of　mean-square　dissipativity.　Finally,　an　example　is　given　for　illustration.　(C)　2015　Elsevier　B.V.　All　rights　reserved.