Abstract: We report on a theoretical study of the K- p -> eta Lambda reaction near threshold by using an effective Lagrangian approach. The role of s-channel Lambda(1670), t-channel K*, and u-channel proton pole diagrams are considered. We show that the total cross section data are well reproduced. However, only including the s-wave Lambda(1670) state and the background contribution from t and u channels is not enough to describe the bowl structures in the angular distribution of the K- p -> eta Lambda reaction, which indicates that there should be higher partial waves contributing to this reaction in some energy region. Indeed, if we considered the contributions from a D-03 resonance, we could describe the bowl structures; however, a rather small width (similar to 2 MeV) of this resonance would be needed.