The on-shell electromagnetic mass splitting of kaons is studied, on the assumption that it is purely electromagnetic in origin, in a Lagrangian model incorporating vector-meson dominance of the hadronic electromagnetic current. A simple symmetry-breaking term in Lagrangian, which preserves the invariance under the photon gauge transformation, gives the vector-meson mass spectrum and the negative φ-ω mixing angle systematically. The result for δmK to order α (fine-structure constant) is cutoff dependent. A relatively low cutoff value, around 1 BeV, is required to yield a physically acceptable result. The discrepancy between the theoretical and the experimental values, δmKth- δmKexpt=5.44-6.22 MeV, is most likely attributable to the high-energy contribution, which was neglected in the present approach.