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 $\phi -\omega$ mixing angle systematically. The result for $\delta m_K$ to order $\alpha$ (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, $\delta {m_K}^{\mathrm{th}}-\delta {m_K}^{\mathrm{expt}}=5.44-6.22\mathrm{}$ MeV, is most likely attributable to the high-energy contribution, which was neglected in the present approach.

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