We study the non-leptonic two-body weak decays of $Lambda_b^0 to p M$ with $ M=(pi^-,K^-)$ and $(rho^-,K^{*-})$ in the light-front quark model under the generalized factorization ansatz. By considering the Fermi statistic between quarks and determining spin-flavor structures in baryons, we calculate the branching ratios (${cal B}$s) and CP-violating rate asymmetries ($mathcal{A}_{CP}$s) in the decays. Explicitly, we find that ${cal B}( Lambda_b^0 to p pi^- ,pK^-)=(4.18pm0.15pm0.30, 5.76pm0.88pm0.23)times10^{-6}$ and ${mathcal{A}_{CP}}( Lambda_b^0 to p pi^- ,,pK^-)=(-3.60pm0.14pm0.14, 6.36pm0.21pm0.18)%$ in comparison with the data of ${cal B}( Lambda_b^0 to p pi^- ,pK^-)=(4.5pm0.8, 5.4pm1.0)times10^{-6}$ and ${mathcal{A}_{CP}}( Lambda_b^0 to p pi^- ,pK^-)=(-2.5pm 2.9, -2.5pm2.2)%$ given by the Particle Data Group, respectively. We also predict that ${cal B}( Lambda_b^0 to p rho^-,pK^{*-} )=(12.13pm3.27pm0.91, 2.58pm0.87pm0.13)times 10^{-6}$ and ${mathcal{A}_{CP}}( Lambda_b^0 to p rho^-,pK^{*-} )=(-3.32pm0.00pm0.14,19.25pm0.00pm0.80)%$, which could be observed by the experiments at LHCb.
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