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In this article,we consider the following coupled fractional nonlinear Schr?dinger system in RN({(??)su+P(x)u=μ1|u|2p?2u+β|v|p|u|p?2u,x∈RN ,(??)sv+Q(x)v=μ2|v|2p?2v+β|u|p|v|p?2v,x∈RN ,u,v∈Hs(RN),)where N ≥ 2,00,μ2>0 and β ∈ R is a coupling constant. We prove that it has infinitely many non-radial positive solutions under some additional conditions on P(x),Q(x),p andβ. More precisely,we will show that for the attractive case,it has infinitely many non-radial positive synchronized vector solutions,and for the repulsive case,infinitely many non-radial positive segregated vector solutions can be found,where we assume that P(x) and Q(x) satisfy some algebraic decay at infinity.