We have investigated kaon photoproduction on a proton and a neutron near their production thresholds by utilizing an isobar model. The background term of the model is constructed from Feynman diagrams, while the resonance term is derived from the multipoles formalism. In the case of the γ + p → K+ +Λ channel we found that both pseudoscalar (PS) and pseudovector (PV) models are able to reproduce the available photoproduction data up to W = 50 MeV above the threshold. The hyperon resonance S 01(1800) is found to be important in improving the agreement between model calculation and experimental data. In the case of double polarization observables Ox, and Oz, our result is in agreement with the finding of Sandorfi et al. In the γ+n → K0 +Λ channel we found that the difference between PS and PV models is sizable for future experiments.