The roughness and irregularity of the surfaces in the protein and enzyme are fractal features that may be characterized by fractal dimensions and mass exponents. The surface fractal dimensions calculated by the variation method are different from those obtained by other methods, since the former is applicable to the self-affine system. Thus the results reported here are reliable for the surfaces. However, the fat fractal and multifractal features of proteins and enzymes are studied by simulation. The surface mass exponents are regarded as another kind of scaling exponent, and the spectrum f(alpha) provides further detailed information about the surfaces of enzyme and protein. The applications of the spectrum f(alpha) to the enzymatic reactions is also discussed.