We present an isobar model for kaon photoproduction on the proton γ p → K+ that can nicely reproduce the available experimental data from threshold up to W = 2.0 GeV. The background amplitude of the model is constructed from a covariant Feynman diagrammatic method, whereas the resonance one is formulated by using the multipole approach. All unknown parameters in both background and resonance amplitudes are extracted by adjusting the calculated observables to experimental data. With the help of SU(3) isospin symmetry and some information obtained from the Particle Data Group we estimate the cross section and polarization observables for the neutral kaon photoproduction on the neutron γ n → K0. The result indicates no sharp peak in the K0 total cross section. The predicted differential cross section exhibits resonance structures only at cos θ = −1. To obtain sizable observables the present work recommends measurement of the K0 cross section with W 1.70 GeV, whereas for the recoiled polarization measurement with W ≈ 1.65–1.90 GeV would be advised, since the predictions of existing models show a large variance at this kinematics. The predicted electric and magnetic multipoles are found to be mostly different from those obtained in previous works. For W = 1.75 and 1.95 GeV it is found that most of the single and double polarization observables demonstrate large asymmetries.