Well-ordered surface structure was prepared on a rutile TiO2(001) surface and investigated on the atomic scale by scanning tunneling microscopy (STM). The surface had a latticework-like structure with rows running along the [110] and [110] directions. Each row consisted of narrow terraces separated by single-height steps on their slopes at both sides. An added-row structural model that consists of Ti7O12 suboxide row added on each narrow terrace of a {114}-microfacet structure was proposed on the basis of atom-resolved STM images as well as local coordination considerations. The added row had 4-fold coordinated and 5-fold coordinated Ti atoms, each of which was observed as a bright spot in STM images. Formic acid molecules adsorbed on both Ti sites, while methanol adsorbed preferentially on the 4-fold coordinated Ti atoms, which may support the validity of the structural model. The latticework structure was proved to be stable against thermal reactions of formic acid and methanol.