As a promising one-dimensional material for building nanodevices, single-wall carbon nanotubes (SWNTs) should be organized into a rational architecture on the substrate surface. In this study, horizontally aligned SWNTs with two alignment modes were synthesized on the same R-plane sapphire wafer by chemical vapor deposition with cationized ferritins as catalysts. In the middle part of the wafer, SWNTs were aligned on the R-plane sapphire in the direction [1101]. At the edge of the wafer, SWNTs were aligned in the tangential direction to the wafer edge. The comparison of these two groups of SWNTs suggests the competition between the two alignment modes and indicates that atomic steps in high density have superior influence on the SWNTs' alignment to the crystal structure on the surface of the sapphire substrate. A "raised-head" growth mechanism model is proposed to explain why catalysts can stay active during the horizontally aligned growth of relatively long SWNTs with the strong interaction between SWNTs and the sapphire substrate.