An effective expansion parameter in quantum electrodynamics, β≡2α/3πln(mµ/mc), is proposed and the convergence of a power series in β is discussed for the anomalous magnetic moment of the muon. The series is shown to be expressed as µ(≡(gµ-2)/2)=α/2π∑∞n=0βn×(1+O(α/π)). Under the unphysical condition, ln(mµ/mc)≫1 and |β|≪1, the leading series can be summed up into the form: \tildeµ=α/2 π(1-β)-1.