An asymptotic solution of the concentration and interface morphology for a deep cellular crystal in directional solidification is obtained by using the matched asymptotic expansion method and multiple variable expansion method, and the effect of anisotropic surface tension on deep cellular crystal growth is studied. Results show that the anisotropic surface tension has a significant effect on the concentration and interface shape of deep cellular crystal growth in directional solidification. As the anisotropic surface tension parameter increases, the concentration near the front part of deep cellular crystal decays and the interface shrinks; when as the concentration near the root increases and the curvature of the interface near the root increases or the curvature radius decreases; and the amplitude of the deep cellular crystal increases. The concentration and interface shape of the deep cellular crystal in directional solidification can be calculated with the results obtained in this paper.