  Recent angle resolved photoemission spectroscopy(ARPES) experiments have
suggested that BiS$_2$ based superconductors are at very low electron doping.
Using random phase approximation(RPA) and functional renormalization group(FRG)
methods, we find that $g$-wave pairing symmetry belonging to A$_{2g}$
irreducible representation is dominant at electron doping $x<0.25$. The pairing
symmetry is determined by inter-pocket nesting and orbital characters on the
Fermi surfaces and is robust in a two-orbital model including both Hund's
coupling $J$, and Hubbard-like Coulomb interactions $U$ and $U'$ with
relatively small $J$ ($J\leq0.2U$). With the increasing electron doping, the
g-wave state competes with both the s-wave $A_{1g}$ and d-wave $B_{2g}$ states
and no pairing symmetry emerges dominantly.
