The expressions of mutual impedance between overhead and underground conductors are a class of oscillatory integrals with infinite upper limits. A fast and high accuracy complex Levin method is proposed for these oscillation integrals based on Levin method,Clenshaw-Curtis formula and a new integration interval division scheme in this paper. The experimental results show that the compound Levin method is not affected by horizontal distance and frequency,and can greatly reduce the computational cost. Thus,It is an efficient method to calculate the oscillatory integral.In addition,this method can be used to calculate the mutual impedance between overhead and underground conductors in ahorizontally multilayered soil.