  We propose to introduce non-minimal gravitational coupling of AD field to
Ricci scalar and discuss its impacts on the Q-balls formation and the
associated gravitational wave(GW) productions. New form of scalar potential for
AD field in the Einstein frame is obtained. We find that, with non-minimal
gravitational coupling to AD field, Q-balls can successfully form even with the
choice of non-negative $K$ parameter for $\xi>0$. The associated GW productions
as well as their dependences on the $\xi$ parameter are also discussed.
