  We study direct CP violating asymmetries (CPAs) in the two-body $\Lambda_b$
decays of $\Lambda_b\to pM(V)$ with $M(V)=K^-(K^{*-})$ and $\pi^-(\rho^-)$
based on the generalized factorization method. After simultaneously explaining
the observed decay branching ratios of $\Lambda_b\to (p K^-\,,\; p \pi^-)$ with
${\cal R}_{\pi K}\equiv {\cal B}(\Lambda_b\to p \pi^-)/{\cal B}(\Lambda_b\to p
K^-)$ being $0.84\pm 0.09$, we find that their corresponding direct CPAs are
$(5.8\pm 0.2,\,-3.9\pm 0.2)\%$ in the standard model (SM), in comparison with
$(-5^{+26}_{-~5},\, -31^{+43}_{-~1})\%$ and $(-10\pm8\pm4,\, 6\pm7\pm3)\%$ from
the perturbative QCD calculation and the CDF experiment, respectively. For
$\Lambda_b\to ( p K^{*-},\, p\rho^-)$, the decay branching ratios and CPVs in
the SM are predicted to be $(2.5\pm0.5,\,11.4\pm2.1)\times 10^{-6}$ with ${\cal
R}_{\rho K^*}=4.6\pm0.5$ and $(19.6\pm1.6,\, -3.7\pm0.3)\%$, respectively. The
uncertainties for the CPAs in these decay modes as well as ${\cal R}_{\pi
K,\,\rho K^{*-}}$ mainly arise from the quark mixing elements and
non-factorizable effects, whereas those from the hadronic matrix elements are
either totally eliminated or small. We point out that the large CPA for
$\Lambda_b\to p K^{*-}$ is promising to be measured by the CDF and LHCb
experiments, which is a clean test of the SM.
