  In this paper we give the decomposition of a martingale under the sublinear
expectation associated with a $G$-L'evy process X with finite activity and
without drift. We prove that such a martingale consists of an Ito integral
w.r.t. continuous part of a $G$-L'evy process, compensated Ito-L'evy integral
w.r.t. jump measure associated with $X$ and a non-increasing continuous
$G$-martingale starting at 0.
