  In this paper, nonlocal symmetries of variable coefficient
Ablowitz-Kaup-Newell-Segur(AKNS) system are discussed for the first time. With
lax pair of time-dependent coefficient AKNS system, the nonlocal symmetries are
obtained, and they are successfully localized to a Lie point symmetries by
introducing a suitable auxiliary dependent variable. Furthermore, using the
obtained Lie point symmetries of closed system, we give out two types of
symmetry reduction and explicit analytic solutions. For some interesting
solutions, the figures are given out to show their dynamic behavior.
