A number of observations have been reported on chemical capture and catalysis of anchoring materials for lithium-sulfur batteries. Here, we propose the design principles for the chemical functioned graphene as an anchor material to realize both strong chemical trapping and catalysis. Through the first principle, the periodic law is calculated from the theory. Seven different co-doping series were investigated, e.g. MN4@graphene (M = V, Cr, Mn, Fe, Co, Ni, and Cu). From binding energy, partial density of state, and charge density difference analysis, the FeN4 and CrN4 co-doped graphene show good performance for the lithium-sulfur battery from both strong anchoring and catalytic effects. For the most kinds of Li2Sx (x = 1, 2, 4, 6, 8) absorption, two combinations can be achieved, including S-bonding and Li-bonding. The competition between the M-S and the N-Li shows the main difference of the co-doped configurations. Moreover, the S-bonding systems have better performance for both moderate chemical trapping and strong catalysis. The binding energies of Li2Sx and Li decomposed properties considered as the key descriptors for the rational design of lithium-sulfur battery. Lastly, we offer design rules for high performance lithium-sulfur batteries based on the chemical functional graphene materials. (C) 2018 Elsevier Inc. All rights reserved.