  We study CP violation in b-baryon decays of $\Xi_b^- \to \Xi^- D$ with $D =
D^0, \bar{D}^0$ and $D_i~(i=1,2)$. We find that these baryonic decay processes
provide an ideal opportunity to measure the weak phase due to the absence of
the relative strong phase. Explicitly, we relate $\bar{\rho}$ and $\bar{\eta}$
the CKM elements with the decay rate ratios of $R_i= \Gamma(\Xi_b^- \to
\Xi^-D_{i} ) / \Gamma( \Xi_b^- \to \Xi^-D^0 )$ without the charge conjugate
states. As a complementary, we also examine the decay distributions of
$\Lambda_b \to \Lambda(\to p \pi^- ) D$. There are in total 32 decay
observables, which can be parameterized by 9 real parameters, allowing the
experiments to extract the angle $\gamma\equiv
\arg(-V_{ud}V_{ub}^*/V_{cd}V_{cb}^*)$ in the CKM unitarity triangle. In
addition, the feasibilities of the experimental measurements are discussed. We
find that $\bar{\rho}$ and $\bar{\eta}$ can be extracted at LHCb Run3 from
$\Xi_b^- \to \Xi^- D$, and a full analysis of $\Lambda_b \to \Lambda(\to p
\pi^-)D$ is available at LHCb Run4.
