Recent results from CDF Collaboration favor a large CP asymmetry in B s → K − π + decay, while the Standard Model prediction is very small. Moreover, the measurement of its branching ratio is lower than the Standard Model prediction based on the QCD factorization. We compute the gluino-mediated supersymmetry contributions to B s → K ( * )− π + ,K ( * )− ρ + decays in the frame of the mass insertion method, and find that for m 2 g m 2 q ≤ 2, the theoretical predictions including the LR and RL mass insertion contributions are compatible with the measurements of B s → K − π + decay and B 0 −B 0 mixing within 2σ ranges. Using the constrained LR and RL mass insertion parameter spaces, we explore the supersymmetry mass insertion effects on the branching ratios, the direct CP asymmetries and the polarization fractions in B s → K * − π + , K − ρ + , K * − ρ + decays.We find the constrained LR and RL insertions can provide sizable contributions to the branching ratios of B s → K * − π + ,K ( * )− ρ + as well as the direct CP asymmetry and the longitudinal polarization of B s → K * − ρ + decay without conflict with all related data within 2σ ranges. Near future experiments at Fermi Lab and CERN LHC-b can test our predictions and shrink/reveal the mass insertion parameter spaces.In the recent ten years, the successful running of B factories BABAR and Belle has provided rich experimental data for B ± and B 0 , which has confirmed the Kobayashi-Maskawa CP asymmetry mechanism in the Standard Model (SM) and also shown hints for new physics (NP). Among the rich phenomena of B decays, the decay modes of B mesons into pairs of charmless mesons are the known effective probes of the CP violation in the SM and are sensitive to potential NP scenarios beyond the SM. The two body charmless B s decays will play the similar role in studying the CP asymmetries (CPA), determining CKM matrix elements and constraining/searching for the indirect effects of various NP scenarios. Recently the CDF Collaboration at Fermilab Tevatron has made the first measurement of charmless two-bodyThe measurement is important for understanding B s physics, and also implies that many B s decay modes could be precisely measured at the LHC-b.Compared with the theoretical predictions for these quantities in Refs. [5][6][7], based on the QCD factorization (QCDF) [8], the perturbative QCD (PQCD) [9], and the soft-collinear effective theory (SCET) [10], respectively, one would find the experimental measurement of this branching ratio agrees with the SM predictions with SCET [5], but lower than the predictions with QCDF and PQCD [6,7]. For the CDF measurement of A dir CP (B s → K − π + ), its central value favors a large CP violation in B s → K − π + decay (different from 0 at 2.3σ), although it is also compatible with zero. In Refs. [11,12], a robust test of the SM or a probe of NP is suggested by comparison of the direct CP asymmetry in B s → K − π + decay.The decays B s → K ( * )− π + , K ( * )− ρ + have been extensively studied in the literatures (for example, [11]...