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We study the rare decays B u ! ' ' ÿ , ' ' ÿ and B 0 d ! ' ' ÿ (' e, ) in the R-parity violating supersymmetric standard model. From the latest upper limits of BB u ! ' ' ÿ and BB 0 d ! ' ' ÿ , we have derived new upper bounds on the relevant R-parity violating couplings products, which are stronger than the existing ones. Using the constrained parameter space, we present the R-parity violating effects on the branching ratios and the forward-backward asymmetries of these decays. We find that BB 0 d ! ' ' ÿ and BB u ! ' ' ÿ could be enhanced several orders by the R-parity violating sneutrino and squark exchanges, respectively. The R-parity violating effects on the dilepton invariant mass spectra of B u ! ' ' ÿ , ' ' ÿ and the normalized forward-backward asymmetry A FB B u ! ' ' ÿ and A FB B u ! ' ' ÿ are studied in detail. Our results could be used to probe the R-parity violating effects and will correlate with searches for the direct R-parity violating signals at the future experiments.