  We investigate CP violation in the purely right-handed b quark to c- and u-
quark coupling model under the constraint of right-handed W-gauge boson mass
M_R > 720 GeV , which is experimentally obtained recently by D0 Collaboration
at Fermilab. By using the data on $K_L-K_S$ mass difference, CP violating
parameter $\epsilon$ in the neutral kaon system and $B_d-\bar B_d$ mixing,
together with the new data of $Br (B^-\to \psi\pi^-) /Br (B^-\to \psi K^-) =
0.052 \pm 0.024 (\approx \mid V_{cd}/V_{cs} \mid^2)$, we can fix all of the
three independent angles and one phase of the right-handed mixing matrix V^R.
Under these constraints, another CP-violating parameter $\epsilon'/\epsilon$
and electric dipole moment of neutron are shown to be consistent with the data
in our model. The pattern of CP violation in the nonleptonic decay of
$B_d(B_s)$ mesons to CP eigenstates is different from that in the Standard
Model.
