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Recent carbon allotropes such as carbon nanotubes (CNTs), fullerenes (C60s) and graphene have attracted great interests in both science and engineering due to their unique properties such as excellent electrical and mechanical properties as well as its vast surface area, and have led to many commercial applications. Especially, CNTs have been considered to be one of the promising candidates in the Li ion battery system because of its outstanding properties. However, the experimental results in the pristine CNT system have shown just slight improvement than original graphitic carbon material, which has been attributed to the weak adsorption of Li on CNTs. In this study, we investigated two types of CNT-C60 hybrid system consisting of CNTs and C60s to improve Li adsorption capabilities and predict its performance through quantum mechanical (QM) computations. First, we investigated adsorption energy of lithium (Li) on dilute CNT-C60 hybrid and CNT-C60 nanobud system as well as various electronic properties such as band structure, density of states (DOS), molecular orbital and charge distribution. Then, we expanded our interest to the more realistic condensed structure of CNT-C60 hybrid and nanobud system to examine actual electrochemical characteristics. The study of the condensed structure has been expanded to the very unique CNT-C60 nano-network system and examined mechanical strength as well as electronic properties. Finally, Li adsorption on other carbon allotropes system such as graphene-C60 hybrid and graphene-C60 bud system was investigated in order to provide fundamental understanding of electronic interaction between carbon allotrope and effect of Li adsorption.