A multi-level layered elongation method was developed for efficiently analyzing the electronic states of local structures in large bio/nano-systems at the full ab initio level of theory. The original elongation method developed during the last three decades in our group has focused on the system in one direction from one terminal to the other terminal to sequentially construct the electronic states of a polymer, called a theoretical synthesis of polymers. In this study, an important region termed the central (C) part is targeted in a large polymer and the remainder are terminal (T) parts. The electronic structures along with polymer elongation are calculated repeatedly from both end T parts to the C central part at the same time. The important C part is treated with large basis sets (high level) and the other regions are treated with small basis sets (low level) in the ab initio theoretical framework. The electronic structures besides the C part can be reused for other systems with different structures at the C part, which renders the method computationally efficient. This multi-level layered elongation method was applied to the investigation on DNA single bulge recognition of small molecules (ligands). The reliability and validity of our approach were examined in comparison with the results obtained by direct calculations using a conventional quantum chemical method for the entire system. Furthermore, stabilization energies by the formation of the complex of bulge DNA and a ligand were estimated with basis set superposition error corrections incorporated into the elongation method.