On the basis of first-principles plane-wave calculations, we examine the adsorption and diffusion of lithium on the hexagonal MoS2(1-x)Se2x monolayers with variation of x for 0.00, 0.33, 0.50, 0:66, and 1.00. We find that the lowest energy adsorption positions of Li adatom is at the top site of Mo atom in both MoS2 and MoSe2 monolayers, while Li moves through the Mo-S bond for MoS2(1-x)Se2x. While bare MoS2(1-x)Se2x compounds are nonmagnetic semiconductor and its energy band gap varies with x, they can be metallized by Li adsorption. NEB calculation results show that their energy barriers make them suitable for using in electrode materials. The lithium adsorption energy is sensitive to the external strain, when we elongate the lattice constants, the adsorption energy decreases quickly. We also examine the penetration energy barrier for single lithium atom to pass through the MoS2(1-x)Se2x monolayers; this barrier is, decreasing from similar to 2.5 eV to similar to 1.3 eV with increasing selenium concentration.