We propose in this paper an alteating A-φ method for the quasi-magnetostatic eddy current problem by means of finite element approximations. Bounds for continuous and discrete error in finite time are given. And it is verified that provided the time step τ is sufficiently small, the proposed algorithm yields for finite time T an error of (h + τ1/2)in the L2-norm for the magnetic field H(=μ-1△× A), where h is the mesh size, μ the magnetic permeability.