We investigate K * Λ(1116) photoproduction off the proton and neutron targets in the effective Lagrangian method in the tree-level Born approximation. In addition to the K, K * , and κ exchanges which are the main contributions to the reaction, we consider the contributions from the higher nucleon resonances D13(2080) and the D15(2200). We find that the D13(2080) plays a crucial role in explaining the enhancement of the near-threshold production rate, which results in a good agreement with the experimental data for the proton targets, while the contribution of the D15(2200) is rather small. A similar conclusion is drawn for K * photoproduction off the neutron targets. In addition to the energy and angular dependence of the cross sections, we present the predictions on the photon-beam asymmetry.