By using periodic rotational striations as a time marker, the initial instability of a planar interface and the development of the cellular interface have been studied in Czochralski growth system of anisotropic LiNbO3 crystals doped with yttrium. The critical condition for very birth of instability of planar interface has been obtained. And there are two kinds of initial perturbations to be observed, that is, sinusoidal perturbation and sinusoidal travelling wave perturbation. Experimental results revealed that the planar interface evolves from sinusoidal perturbation to facetted perturbation to coarse facetted perturbation, finally, to stable cellular interface. It has been found that the wave-length of stable cellular interface is different from that of initial perturbation and always integral times larger than that of initial one. There is also a difference to be found between critical velocity of the plane-to-cell transition and that of cell-to-plane transition for a same crystal grown from the same system. It may be implied that the facetted cell is more stable than the nonfacetted plane.