  We calculate for the first time the electric dipole moment (EDM) of the
$^6$Li nucleus within the alpha + p + n three-body cluster model using the
Gaussian expansion method, assuming the one meson exchange P, CP-odd nuclear
forces. It is found that the EDM of the $^6$Li is 2 times more sensitive on the
isovector pion exchange P, CP-odd nuclear force than the deuteron EDM, due to
the CP-odd interaction between the nucleons and the alpha cluster. The $^9$Be
EDM is also calculated in the same framework as an alpha + alpha + n three-body
system. We also test the ab initio calculation of the EDM of the deuteron,
$^3$H and $^3$He nuclei using the realistic Argonne $v18$ nuclear force. In the
ab initio calculations, good agreements with previous studies are obtained. We
finally discuss the prospects for the new physics beyond the standard model.
