In order to investigate the effect of the structure of fractal substrates on dynamic scaling behavior of the surfaces, the etching model growing on the Sierpinski arrowhead and crab fractal substrates is simulated by means of Kinetic Monte Carlo (KMC). It is found that the etching model evolving on two kinds of fractal substrates can exhibit dynamic scaling behavior, and can still be described by the Family-Vicsek scaling relation. Although the Sierpinski arrowhead and crab fractal substrates have the same fractal dimension, the obvious different values of roughness exponent and dynamic exponent z, however, are obtained on these two substrates, and they neither of them satisfy the scaling relation +z=2, which is satisfied in the usual Euclid space. It can be seen from the results obtained here that the scaling exponents of the etching model growing on fractal substrate are determined by not only the fractal dimension but also the fractal structure.