  We consider two-dimensional Brans-Dicke theory to study the initial
singularity problem. It turns out that the initial curvature singularity can be
finite for a certain Brans-Dicke constant $\omega$ by considering the quantum
back reaction of the geometry. For $\omega=1$, the universe starts with the
finite curvature scalar and evolves into the flat spacetime. Furthermore the
divergent gravitational coupling at the initial time can be finite effectively
with the help of quantum correction. The other type of universe is studied for
the case of $0<\omega<1$.
