Some scaling behaviors of a fractal resistor network are studied based on a hierarchical model with an exponentially wide distribution obeying g=g0eWx. We analyse the effects of the disorder width W on the overall resistance and the moments of distributions, and corresponding universal curves are found. We regard the problem as a crossover behavior between the competing effects of the size of the network and the width of the distribution of conductances. Our results are in good agreement with the numerical simulation reported by Tong on Sierpinski honeycomb network.