The {0001} face develops on the habit of self-frequency doubling laser crystal Yb: YAl3(BO3)4 (YbYAB) only under high growth rate condition, and its morphology is rough. To study the growth mechanism of {0001} face, we have observed the growth morphology on {0001} polishing section by atomic force microscopy (AFM). A series of AFM images captured in different growth durations on the {0001} polishing section reflect the crystal growth process. It is shown that the growth morphology on the {0001} polishing section was rough with many hillocks at the first growth stage, and it can become smooth finally, although the growth morphology on the {0001} face developed naturally on YbYAB crystal habit is always rough. On the smooth {0001} surface formed at the last growth stage, there are some triangular pits. This fact is different from that of hillocks in most crystal growth morphologies. AFM can easily distinguish the pits or hillocks on the surface, but differential interfere contrast microscopy (DIC) can not do. The orientation of the triangular pits is just the opposite to the triangular {0001} faces. The chemical etching pattern is also composed of this kind of triangular pits. These growth morphology and etching pattern of the {0001} faces show 3m symmetry, but the point group of YbYAB crystal is 32. The symmetric contradiction between morphology and point group does not exist for quartz, although which has the same point group as YbYAB. From quartz {0001} surface morphology we can distinguish the right form or left form of the crystal, but from YbYAB {0001} surface morphology we can not do. The reason for the symmetric contradiction between YbYAB {0001} surface morphology and its point group is not known yet.