  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 ${\cal B}(
\Lambda_b^0 \to p \pi^- ,pK^-)=(4.18\pm0.15\pm0.30,
5.76\pm0.88\pm0.23)\times10^{-6}$ and ${\mathcal{A}_{CP}}( \Lambda_b^0 \to p
\pi^- ,\,pK^-)=(-3.60\pm0.14\pm0.14, 6.36\pm0.21\pm0.18)\%$ in comparison with
the data of ${\cal B}( \Lambda_b^0 \to p \pi^- ,pK^-)=(4.5\pm0.8,
5.4\pm1.0)\times10^{-6}$ and ${\mathcal{A}_{CP}}( \Lambda_b^0 \to p \pi^-
,pK^-)=(-2.5\pm 2.9, -2.5\pm2.2)\%$ given by the Particle Data Group,
respectively. We also predict that ${\cal B}( \Lambda_b^0 \to p \rho^-,pK^{*-}
)=(12.13\pm3.27\pm0.91, 2.58\pm0.87\pm0.13)\times 10^{-6}$ and
${\mathcal{A}_{CP}}( \Lambda_b^0 \to p \rho^-,pK^{*-}
)=(-3.32\pm0.00\pm0.14,19.25\pm0.00\pm0.80)\%$, which could be observed by the
experiments at LHCb.
