Motivated by the first measurement on B（Bs→ Ф μ^＋ μ^-by the CDF Collaboration, we study the supersymmetric effects in semi-leptonic Bs→ Ф μ^＋ μ^-ecay. In our evaluations, we analyze the dependences of the dimuon invariant mass spectrum and the forward-backward asymmetry on relevant supersymmetric couplings in the MSSM with and without R-parity. The analyses show that the new experimental upper limits of B（Bs→ Ф μ^＋ μ^-from the LHCb Collaboration could further improve the bounds on sneutrino exchange couplings and （δ^u LL）23 as well as （δ^d LL,RR）23 mass insertion couplings. In addition, within the allowed ranges of relevant couplings under the constraints from B（Bs→ Ф μ^＋ μ^- B（B → K^（＊） μ^＋ μ^-and B（Bs → μ^＋ μ^-, the dimuon forward-backward asymmetry and the differential dimuon forward-backward asymmetry of Bs→Ф μ^＋ μ^-re highly sensitive to the squark exchange contribution and the （ LL）23 mass insertion contribution. The results obtained in this work will be very useful in searching for supersymmetric signals at the LHC.
