In this paper, a novel method for accelerating frequency sweeping in eddy current calculation using finite elements method (FEM) is presented. Exploiting the fact that between adjacent frequencies, the eddy current distributions are similar, an algorithm is proposed to accelerate the frequency sweeping computation. The solution of the field quantities under each frequency, which involves solving a system of linear equations using the Conjugate Gradients Squared (CGS) method, is accelerated by using an optimized initial guess – the final solution from the previous frequency. Numerical tests show that this treatment could speed up the convergence of the CGS solving process, i.e. reduced number of iterations reaching the same relative residuals or reaching smaller residuals with the same iteration number.