We calculate for the first time the electric dipole moment (EDM) of the Li6 nucleus within the α+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 Li6 is 2 times more sensitive to the isovector pion exchange P, CP-odd nuclear force than the deuteron EDM because of the CP-odd interaction between the nucleons and the α cluster. The Be9 EDM is also calculated in the same framework as an α+α+n three-body system. We also test the ab initio calculation of the EDM of the deuteron, H3, and He3 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 new physics beyond the standard model.