We study the fractal structure of the surface in two-dimensional quant
um Regge calculus by performing Monte Carlo simulation with up to 200,
000 triangles. The result can be compared with the universal scaling f
unction obtained analytically in the continuum limit of dynamical tria
ngulation, which provides us with a definite criterion whether Regge c
alculus serves as a proper regularization of quantum gravity. When the
scale-invariant measure is taken as the measure of the link-length in
tegration, we observe the correct scaling behavior in the data for the
type of loop attached to a baby universe. The data seem to converge t
o the universal scaling function as the number of triangles is increas
ed. The data for the type of loop attached to the mother universe, on
the other hand, shows no scaling behavior up to the present size.