R_b and R_l in MSSM without R-Parity

We examined Z\ell^+\ell^- and Zb\bar b couplings in the minimal supersymmetric model (MSSM) with explicit R-parity violating interactions. We found the top quark L-violating couplings \lambda'_{i3k} and B-violating couplings \lambda''_{3j3} could give significant contributions through the top quark loops. To accomadate the latest R_{\ell} data, \lambda'_{i3k} are suject to stringent bounds, some of which can be much stronger than the current bounds. Within the current perturbative unitarity bound of 1.25 for \lambda''_{3j3}, the R_b value in R-violating MSSM agrees well with the experimental data at $2\sigma$ level, but may lie outside the 1\sigma range depending on the involved sfermion mass.