Crystal growth is a process in which the growth elements from the ambience cross the interface and enter crystal lattices. In general, the entry of the growth elements into the crystal lattice through the interface constitutes a key problem in the study of interfacial structure of crystal growth.It is held in this paper that the growth elements (molecules or atoms) walk at random in ambience. On the basis of the true self-avoid walk (TSAW) model and the principle of renormalization, the authors studied fractal behavior of interfacial structure of crystal growth. It is found that fractal behavior of interfacial structure of crystal growth has a close relationship with the shape of the walking route of the growth elements, and that there exists a close similarity in fractal dimension between TSAW and standard Koch curve under the ideal condition.