Monolayer Molybdenum Disulfide (MoS2) is a promising anode material for lithium ion batteries because of its high capacities. In this work, first principle calculations based on spin density functional theory were performed to investigate adsorption and diffusion of lithium on monolayer MoS2 with defects, such as single- and few-atom vacancies, antisite, and grain boundary. The values of adsorption energies on the monolayer MoS2 with the defects were increased compared to those on the pristine MoS2. The presence of defects causes that the Li is strongly bound to the monolayer MoS2 with adsorption energies in the range between 2.81 and 3.80 eV. The donation of Li 2s electron to the defects causes an enhancement of adsorption of Li on the monolayer MoS2. At the same time, the presence of defects does not apparently affect the diffusion of Li, and the energy barriers are in the range of 0.25-0.42 eV. The presence of the defects can enhance the energy storage capacity, suggesting that the monolayer MoS2 with defects is a suitable anode material for the Li-ion batteries.