  In order to clarify superconducting properties of BiS$_2$-based layered
superconductors LaO$_{1-x}$F$_x$BiS$_2$, we evaluate the superconducting
transition temperature $T_{\rm c}$ and analyze the gap function in a
weak-coupling limit on the basis of the two-dimensional two-orbital Hubbard
model. It is found that $T_{\rm c}$ becomes maximum at $x=0.6$ in the present
calculations. For $x<0.45$, we obtain the $d$-wave gap of which line nodes do
not cross the pocket-like Fermi-surface curves with the centers at X and Y
points. On the other hand, for $x>0.45$, the extended $s$-wave gap is found for
a couple of large Fermi-surface curves with the centers at M and X points. The
variation of the Fermi-surface topology plays a key role for the gap symmetry
in BiS$_2$-based superconductors.
