The effects of the weak interaction on the electromagnetic properties of leptons are discussed. The theory of the vector meson developed by Stueckelberg and Matthews and Schwinger's gauge-invariant method are applied to the interactions' between leptons, the electromagnetic field and the intermediate boson. The matrix elements accurate to first order in e and G are given. The corrections to the anomalous magnetic moments of the charged leptons obtained in the present work are free from divergence. The ambiguity appearing in zeldovich's work is not present.